Hilton has usually been quite good with proper documentation (or else everybody reading this thread would call up and say their dad was in the hospital and ask for a refund when plans changed).

They will probably take something very simple like

To whom it may concern:

Mr John Smith is currently under my care at such and such a hospital at this time.

As long as it's on something official looking you will get the refund.

I don't believe they are asking for anything confidential or anything, it's not like they want to review the medical records.

I believe you will find it's quite a common occurance, a request like this for confirmation.