So she took you overtime the week before and said she would shorten your next appointment to make up that time. But when she did actually shorten it, she justified doing so on the grounds of saying she had another appointment rather than admitting it was to make up the overtime from the week before.

Seems messy. I think Ts should be responsible for ending on time, and cutting your next session short seems unwarranted to me. However, I guess conventions could differ in different countries and/or cities.