OK, so it was upsetting but it was your mistake and it's annoying you have to pay but that is a standard policy of most professionals as they have to earn an income and if they have no shows, they aren't earning money to even pay their overheads at their office.

There is a lot of talk around here about boundaries set by both T's and clients. Her expectations were clearly explained to you, and the consequences were clearly outlined beforehand. You did not meet your end of the bargain and in my opinion sleeping in doesn't cut it as an excuse and 8am is not that early for an appointment, if she arrived late to an appointment because she slept in how would you feel?? you would be complaining that you felt abandoned, don't trust her etc etc.
If she can only offer a 8am appointment she must be busy and may even have many patients trying to see her and has to say no to people, so if she agrees to see you, you have to turn up otherwise there are other people who are looking for T's and would turn up on time.

If you got hold of her on the phone with 15min left of your session I think it was right that she did not start talking T things in such a short time when other practical issues like rescheduling and payment issues needed to be discussed.

Just think of it as a life lesson, there are consequences to your actions, even sleeping in and you will learn from your mistake and maybe set 2 alarms or some other tactic to enable you to arrive on time to things in the future.