I don't see how anyone insinuated or blamed anybody. She called to find out why kid isn't picked up. And she hung up because she worried about her kid. I think it's your perception that it was about you rather than safety of her child.

Personally I'd call mom from the parking lot that the kid isn't there. I wouldn't sit there for 5 hours waiting but I'd give mom heads up.

I found it a bit strange that you simply went home and never contacted a parent and she only found out an hour later that he still isn't picked up. It's understandable she got worried. She was in fact rather nice about it. Some parents wouldn't be as nice.

Also keep in mind even the nicest kids make stuff up and cover for each other. As an adult you have to double check things.

Why are you doing it in the first place? A favor? Getting paid?