I am quite sure that for me an admission of guilt is all some people are able to do and that this is their genuine way of apologising.
For me, I would expect a sorry. At the end of the day it doesn’t matter whose fault it is, your appointment has been given away again. Mistakes happen but at whose expense, seems that both times have been at your expense. I would be angry and feel dismissed. I think I would expect my t to really meet me here and call me in even for an hour after her working hours and to really hear my hurt and anger in person not to apologise over a text.
I don’t know about you but this experience would be extremely hurtful as I struggle with a huge message of ‘I don’t matter’ and ‘my feelings are not important’. This experience would only reiterate those beliefs and o would need my t to really see that and hear that.