Actually, the Oath requires allegiance to the Constitution of the United States.

"I, [name], do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.

The Admiral also conveniently forgets that the obligation is to obey "Lawful Orders."