Honestly, I wouldn't do what she did, but I can see why she did it. She tried everything everyone here would have suggested and it didn't work. She tried Felineway, she tried putting him in a room and retrain him, she took him to the vet numerous times. Living with cats that insist on pooping on the floor (right after I clean the litter box) and peeing on the counters, the dog food dishes and the bathtub, I can understand how it can just be too much....especially after having to spend all that money on recarpeting just to have the cat start peeing on the bed (I have one that does that too).
If she took him into a regular shelter and told them why she is bring him in, they would have smiled, said they would do their best, and put him to sleep as soon as she left. That was not a cat that could be rehomed. The fact that he was "throwing" himself against the door when he was in the basement with food, water, litter box and bedding makes me think something was wrong with him. What cat, when put into a new room, won't go exploring? The LAST thing most would do is make a fuss until they got familiar with the room.
I can understand why she made that decision, but I do think she should have found a no kill shelter instead.