My long term T's have never had a problem apologizing to me, though I don't remember much about the others. My last T apologized for having to cancel an appointment (only twice- once a family thing & once because she was sick). She also apologized a few times about not responding to a message I sent (various reasons- didn't realize I wanted a response, battery died and got message days later, etc.). She wouldn't just apologize for nothing though and didn't let me either. I appreciated her being able to admit to her mistakes.

It sucks that your T tried to blame you here. I feel like that's not a T thing, but just something that certain people do. I've had to learn to accept responsibility myself.