Sounds like he is trying to have a pissing contest with you or someone on the staff. And even if you were testing him, that is ok. It happens and it is not like you started the hospital stuff. That would be different. Sounds like the hospital was as much his idea as yours. the fact that he was too busy to start the process forms throws up some red flags for me.

Go to your appointment and figure this out. Best to discuss in person. Good luck!