I have to admit that I was wondering if, after the negotiations failed, a few good Seals just said, eff it, let's do what needs to be done before the savages kill the Captain. They may have been given the go ahead, but if not, would even The One dare to complain publicly.
Sorry, SEAL commanders don’t make a move without higher authority. That didn’t happen. However, the highest ranking Naval officer in the vicinity could have made the decision. I doubt in came from the WH.