Certainly she can ask HR what she can do, recognizing that HR likely had nothing to do with her initial enrollment. I have my doubts about prospects for success, but there's no harm in asking.
CMS (Centers for Medicare and Medicaid Services) is the Medicare regulatory agency (authority) within HHS much as the IRS is the taxation regulatory agency within the Treasury Dept. And much as the IRS puts out Pubs which can have errors (they are not the regulations themselves), CMS puts out material for public consumption that can have errors. In both instances, errors are not common but they're certainly possible.
So when CMS says that disenrolling from non-premium Part A Medicare is against the law, it's possible that this agency is misstating its own regs. Not likely, but possible.
Here's CMS form 1763 for terminating Medicare coverage.
https://www.cms.gov/medicare/cms-forms/cms-forms/downloads/cms1763.pdf
It is titled: REQUEST FOR TERMINATION OF PREMIUM PART A, PART B, OR
PART B IMMUNOSUPPRESSIVE DRUG COVERAGE
It begins:

WHO CAN USE THIS FORM?
People with Medicare premium Part A or B who would like
to terminate their hospital or medical insurance coverage.

Is it possible that there's a different form for non-premium Part A beneficiaries to terminate coverage? Sure, but not likely since this form covers all other situations.
We can go back to the Wellesley College page with info from HSA Resources to observe some oddities.
First, this is an old page (not disqualifying, but curious). The pdf creation date is  11/22/2016. That's consistent with the fact that HSA Resources was acquired by Select Account in Dec 2016.
(FWIW, SelectAccount was renamed Further and acquired by HealthEquity in 2021.)
More important is how it suggests that disenrollment is dated differently depending on whether one is receiving SS checks. If you are receiving checks, it says that you are supposed to pay back any Medicare money spent on claims. Effectively, this is undoing the Medicare enrollment entirely. OTOH, it doesn't say that you have to refund Medicare benefits received if you're not receiving SS checks. It seems you are allowed to keep Medicare benefits received up to the time of disenrollment request.
What this page is doing is misquoting the rules for undoing registration for Social Security (not Medicare) benefits:

The request to withdraw a [Social Security retirement] application must be made in writing. Anyone who receives benefits based on the client's application must consent in writing to the withdrawal. Additionally, all benefits previously received must be repaid. This includes:

• Benefits received by family members;
  
• Money withheld for Medicare premiums;
  
• Money withheld for voluntary tax withholding; and
  
• Money withheld for garnishments.

https://www.journalofaccountancy.com/news/2023/mar/how-to-reverse-course-collecting-social-security.html
You have to repay the Medicare premiums not the Medicare benefits, from start until termination. That is, you have Medicare throughout, but the premium payments come from you and not your Social Security check if you undo those checks. And it terminates SS benefits, not Medicare enrollment.
The one item I have found that supports the idea that any Medicare Part A can be voluntarily terminated is in the Medicare statute itself (42 U.S. Code § 1395q(b)(1)):

An individual’s coverage period shall continue until his enrollment has been terminated—
(1) by the filing of notice that the individual no longer wishes to participate in the insurance program established by this part,

https://www.law.cornell.edu/uscode/text/42/1395q
That says only that such a filing will terminate coverage. It doesn't specify the conditions under which such filing is permitted. Such as being charged a Part A premium. Those conditions may be in the regs, which gets us right back to CMS.

There are secondary sources that go over into HSA and Medicare details. Info is probably also hidden in some obscure federal publications. For your friend, it may matter more what her HR says.
https://offices.depaul.edu/human-resources/benefits/Documents/HSA-medicare-faqs.pdf
https://www.medicareinteractive.org/get-answers/coordinating-medicare-with-other-types-of-insurance/job-based-insurance-and-medicare/health-savings-accounts-hsas-and-medicare

There's no requirement that HSA contributions be made into the employer's HSA. She can open an outside HSA (say, at Fidelity) for the year. The benefits of contributing to an employer's HSA via payroll deduction are:
1. Possible employer contribution
2. Reduction in payroll income subject to FICA
     a) Social Security (6.2% employee-side) - someone in the 32% tax bracket would likely max out even if W2 income is reduced by HSA contribution amount
     b) Medicare (1.45% employee-side) - this is the only obvious benefit of contributing to the employer's chosen HSA.
---
Color me skeptical about being able to disenroll from Part A. The referenced page is not authoritative and was shown to be imprecise (re: Part C premiums). To offer another non-authoritative page, here's an AARP page. It says that one cannot generally drop part A if one is not paying a premium, even if one has an employer plan providing primary coverage.
The hedging there is in the word "generally". AARP is just repeating what Medicare.gov says: "Generally, you can only drop Part A (Hospital Insurance) if you have to pay a premium for it."
However, CMS is unambiguous: "Individuals entitled to premium-free Part A cannot voluntarily terminate their Part A coverage. This is not permitted by law. "
https://www.cms.gov/medicare/enrollment-renewal/health-plans/original-part-a-b
(last modified 9/6/2023)
For a longer narrative saying the same thing, see this Forbes piece, Can You Drop Part A?, 6/9/2023.
https://www.forbes.com/sites/dianeomdahl/2023/06/09/can-you-drop-medicare-part-a/

@yogibearbull, for some reason, I am under the impression that her employer only allows "enrollment" once per year in January. Hopefully, I am wrong.
As davidsherman said "HSA is superior to IRA and Roth IRA". This seems to be the case because unlike an IRA where you are tax upon withdrawal, with an HSA you are not taxed on the income for the contribution or the distribution so long as it is a qualifying medical expense. Am I characterizing this correctly?

@Mona, actually, she can also contribute $4,850 for 2023 by 4/15/24 so long as she signs up for HSA BEFORE December 1, 2023. Fido link has details.
Annual contributions are adjusted each year, so they may be higher in 2025, 2026,...
Tax math looks OK otherwise.

HSA annual contribution limits are (single/family):
2023 $3,850/7,750
2024 $4,150/8,300
There is also additional $1,000 catchup for 55+.
https://www.fidelity.com/learning-center/smart-money/hsa-contribution-limits

She is single and would be able to contribute the full amount of $5,150 in 2024. In a 32% tax bracket, does that mean she would be saving $1,648 in taxes?
And, assuming that she works 3 more years and for easy math, have $15,450 ($5,150 x 3) available for qualifying medical expenses (deductibles, co-payments, etc.)?

One huge benefit of HSAs is years of buildup of funds ....

If she is only going to work 2-3 more years, I wonder if it is worth her while to sign up for the HSA now and deal with unenrolling from Medicare Part A with the Social Security Administration. However, she is in a 32% tax bracket.

Average life expectancy for a US female aged 65 is about 20 years (shorter than 2/3 of the other OECD countries). That's two decades of appreciation.
Even a non-spouse heir can withdraw the HSA assets tax-free, so long as she keeps records of qualifying expenses. The heir must make the withdrawals within a year of death.
https://tax.thomsonreuters.com/blog/what-happens-to-the-funds-in-an-hsa-after-the-account-holder-dies/

This link seems to cover a lot of the questions regarding HSA and turning 65
hsa_and_medicare

At age 65, you can use your HSA to pay for Medicare parts A, B, D and Medicare HMO premiums tax-free and penalty-free.

You can use an HSA to pay for Medicare PPOs and Medicare PFFS plans as well as Medicare HMO plans. They are all types of Part C (Medicare Advantage) plans.
A common misconception is that all Medicare Part C plans are HMOs. This is why one often sees articles saying that a disadvantage of Medicare Advantage (MA) plans is that they limit you to doctors in a network. That's true for HMO plans but not for the other types of MA plans. The PPOs still require insurer approval for some procedures, though.

HSA annual contribution limits are (single/family):
2023 $3,850/7,750
2024 $4,150/8,300
There is also additional $1,000 catchup for 55+.
https://www.fidelity.com/learning-center/smart-money/hsa-contribution-limits

@Mona, yes, HSA contributions are not allowed while on Medicare.
Employers may now require Medicare signup for eligible employees. Mine kicked me out of the group plan as soon as I became Medicare eligible (as a retiree).
One huge benefit of HSAs is years of buildup of funds and that won't happen with late signups.

If she is only going to work 2-3 more years, I wonder if it is worth her while to sign up for the HSA now and deal with unenrolling from Medicare Part A with the Social Security Administration. However, she is in a 32% tax bracket.

@yogibearbull, she is still employed (she figures at least two more years) and her employer does not require her to sign up for Medicare. She signed up for Medicare Part A when she turned 65 to get it out of the way and because it was free, not thinking that she may be interested in an HSA. Her employer seems to be cutting healthcare costs by increasing her contribution and changing to a Blue Cross plan with higher co-pays and deductibles.

@bee
Thanks for the link.
"Stopping Medicare to Reclaim HSA Eligibility
If you signed up for Medicare Part A and now want to decline it, you can do so by contacting the Social Security Administration. Assuming you have not begun receiving Social Security checks this will reestablish your eligibility for an HSA. If you have applied for or have begun receiving Social Security, you cannot opt out of Medicare Part A without paying the government back all the money you received from Social Security payments plus paying the government back for any money Medicare spent on your medical claims. This action will also stop future Social Security payments (until you reapply and start this cycle over again)."
She has not begun receiving Social Security checks, so she would need to contact the Social Security Administration to now "decline" Medicare Part A, in order to reestablish her eligibility for an HSA. Is there any downside to doing this?

@Mona, yes, HSA contributions are not allowed while on Medicare.
Employers may now require Medicare signup for eligible employees. Mine kicked me out of the group plan as soon as I became Medicare eligible (as a retiree).
One huge benefit of HSAs is years of buildup of funds and that won't happen with late signups.

@Mona,
This link seems to cover a lot of the questions regarding HSA and turning 65
hsa_and_medicare

I have a friend who turned 66 in May, her employer's health insurance plan is an HSA-eligible plan, and she is looking to contribute. However, when she turned 65, she signed up for Medicare Part A.
My understanding is that can't participate in Medicare Part A (or B) and contribute to an HSA at the same time. Is this correct? If so, would it make sense to unenroll (if possible) from Medicare Part A?

I have stated that HSA are the single best investment for folks to utilize. If they have to pick one, HSA is superior to IRA and Roth IRA.

Highly recommend Fidelity HSA platform as a choice.

Check out the M* HSA article that YBB referenced.
M* has published annual evaluations of HSA providers since 2017.
ISTR that the Fidelity HSA was always rated high as an investment vehicle.
FWIW...

Wanted to highlight that June MFO had an article by Mark
https://www.mutualfundobserver.com/2023/06/the-young-investors-secret-weapon-the-hsa/

Fidelity, I believe has HSA accounts. Many others too, but I think there are fees associated to these accounts. @bee used to talk about HSA's a lot. He would know more.