I read lots of post from people with "buyers remorse" on advanced purchase rooms.
While I am very sympathetic to your personal situation and sincerely hope you father recovers well, I do not see where this is the hotels problem.
The fact they are willing to even discuss refunding it and have asked for some documentation seems more than reasonable. They could easily just say no
The hotels offer these prices for one reason, to secure business on slow times. The price tag that comes with it is that it is non-refundable.
Stop and think how many bogus claims or people attempting to cancel they would have if they were not strict on this policy. People would always book the advanced purchase rate and feel they could cancel.