Really nice letter, wrong country/state to live in. As I understand it they can dismiss you for no reason at all, and to-keep-Ms.-_____-happy may well be a good reason in their minds since you were quite new.
However there is one thing you didthat I'd like to point out for your future
I assumed that any available seat was free
I assumed would be briefer than it was
I assumed that it was understood that I bore no fault
Always get organisational things in writing. Never assume, check and record. Don't trust anyone's intentions. If you had more of a paper trail instead of he said, she said then the letter would be stronger still. This lesson is one I've learnt from my time at university, I kept assuming people would follow procedures, or they would do what I'd asked them to do, and it screwed me over tens of times.
