The IRS states in the instructions for form 1099-SA:
"As the trustee or custodian, you do not have to allow beneficiaries to return a mistaken distribution to the HSA. However, if you do allow the return of the mistaken distribution, you may rely on the account beneficiary's statement that the distribution was in fact a mistake. See Notice 2004-50, 2004-33 I.R.B. 196, Q/A-76, available at IRS.gov/irb/2004-33_IRB/ar08.html. Do not report the mistaken distribution on Form 1099-SA. Correct any filed Form 1099-SA with the IRS and the account beneficiary as soon as you become aware of the error."
See page 1 at https://www.irs.gov/pub/irs-pdf/i1099sa.pdf
The way this is worded gives the HSA administrator broad latitude on what they can accept as a mistaken distribution. The net effect of this wording is to give an HSA administrator a way to refuse to accept the mistaken distribution if the circumstances do not match what a "mistaken distribution" should be, but it clearly allows the HSA administrator - if it so chooses to spend the time and money - to just accept that the distribution was mistaken and continue with the process.
Thus my advice to give the HSA administrator motivation (keeping a large client happy in return for a small favor) to accept the return of the mistaken distributions and to update the requisite forms.
