Let me add my voice to the choir and say how sorry I am that you are going through all of this. Were it not for the fact that the calendar is unfavorable to you given that the October 15th deadline for pension filings is fast approaching you might have much more participation in this thread.
Also, please recognize that those of us who use our real names might also be restricted not only from discussing when or how something might rise to the level of a crime but also from discussing the matter focusing on merely unethical conduct.
With that said, I can't believe you are the first person seeking treatment from your treatment center of choice to face this issue. Have you asked them if they have already developed a completely ethical solution? Just thinking out loud here but maybe they are willing to send you summary billings from an associated doctor who uses a location other than the treatment center itself for his/her address? "Medical treatment" might be all that is necessary to satisfy the 401(k) gatekeepers, be they Fidelity or somebody associated with the plan's Administrative Committee.
Here are a couple of links you might find interesting:
https://www.employeefiduciary.com/blog/hardship-401k-distributions-frequently-asked-questions
and
https://www.irs.gov/pub/foia/ig/spder/tege-04-0217-0008.pdf
Having both at hand will better arm you in your battle to legally and ethically arrange for your hardship distribution.