When my OH was admitted to hospital for a couple of days his behaviour apparently became ‘very challenging’ to quote the nurse! They had no idea he had dementia, (though it must have been in his notes). I discovered that he’d been demanding that he be allowed to go home now, he was fine and he’d told them he’d get the bus home. I told them under no circumstances should he be allowed to discharge himself, I had to be consulted about anything.
As soon as I mentioned that I had POA and I WOULD use it if needed, everything changed, I had to bring in a certified copy that they’d photocopy for their records and give back and it would help considerably in any dealings they had with him.
I feel pretty sure that, as others have said, in your case they are covering themselves if they have a copy of the POA. It makes everyone’s lives easier as you have authority if any decisions are needed.