is no rule book that says how things like this have to be done. Period.

It’s fair to say you don’t like how they are doing it, I think we all agree with that, but they are not breaking any rules, or even any organizational norms by doing it the way it sounds like they did. In the real world, your manager fires you—even if his/her manager is the one who called for, or signed off on you being let go. Also, in the rest of the world, a manager can fire their subordinates without requiring their boss to “make the call.”