My T once was significantly late starting our appointment because he had a sudden crisis pop up. I was given a prompt apology and brief explanation and I received my full time. He is rarely late.

I find what your T did unprofessional. Crisis management plans should be in place in general. If the person was there threatening harm to themselves or to another person then either the colleague needed to deal with it or they needed to call to have this person taken to the hospital.

I'm trying to imagine a scenario where it would be okay for a T to a) interrupt a session to go deal with something else and b) not to make up that time.

I'm coming up blank honestly.

Even if I can't come up with a scenario, the latter is utterly unacceptable. If the time couldn't be made up right then and there with genuine apology, then they should have offered a time that works for your schedule and you shouldn't be charged for the session that they interrupted.

Your T should have known better.