Wrong tense. There was a coup.
The Commander in Chief took his orders from the military, not the other way around. (Assuming Ulsterman is accurate).
Anyone who has seen the situation room photo knows this at a visceral level.
A petulant little boy sits in the corner while the adults run things.
I have several family members in the military, including a family member who is currently instructing Virginia class submarine crews on launch procedure.
There is simply a point where rational people assume control and maintain a system that is reliant on itself, or dead. It is not a takeover. It is a self perpetuating system based on the hard reality.