Well, they did order a nuclear strike on Manhattan without refering the White House in any way, and the real-life Pentagon refused to cooperate with the Avengers movie for exactly that ambiguity.
SHIELD didn't order the nuclear strike. The nebulous Council they reported to ordered the strike, and Fury, the head of SHIELD, refused to obey that order.
But the SHIELD pilot did.
Technicalities aside, the larger point remains: just who is this Council that either presumes to speak for the White House, or considers themselves above them?