Oh, well, sure, then by definition they have the right to fire her for wearing the wrong color shirt or something - and I'm not sure how that answers the question of how they're justified in firing her for exposing ... nothing at all about her students.
Now imagine it - students all knowing that it doesn't freaking matter that they don't amount to squat; they'll never have to face it.
But my point is a lot weaker than I thought it was - I had the impression (not having read the freaking original blog) that her blog was also anonymous. If it was plain who she was and where she taught, then yeah, that's a serious problem that requires disciplinary action.