Boards have the power to decide any and everything in a corporate structure. They are, in fact, the only way that a decision of the corporation is made and made official.
I'm not sure what legality has to do with any of this. A corporation is a legal structure, and a board is its decision-making body. If you're talking about criminal charges or disputes between parties about who's got the power or authority to do something, then those are decided by courts, but in a civil context courts don't originate decisions. Courts ratify decisions or choose between dissenting views on what the decision is.
The members of the board should have recognized the special nature of this situation, and take the only principled course of action possible here: resign and sue to have the CEO removed and barred; instead they let the interim CEO give himself a golden parachute (so much for protecting the shareholders, he was protecting his arse).
The CEO can't fire the board. The board can fire the CEO.
The majority of shareholders can fire the board.
The fact that one person plays the role of two of those actors is interesting but one of the whole points of corporate governance is that everybody plays their actual role when they're in that role and assigned to do that role.
In that context the board tasked with making a decision on who should be CEO made a defensible decision and then they were fired by the shareholders who disagreed. This is exactly what's supposed to happen. Everything is by the book.
He can when he's the majority shareholder.
> but one of the whole points of corporate governance is that everybody plays their actual role when they're in that role and assigned to do that role.
Where do you think you are ? In Victorian England where everyone dutifully plays one's role with a stiff upper lip and never tries to abuse power ?