It is not clear whether Conway conveyed the terms of the deal to his superiors in Baghdad and at the Pentagon, or even to leaders of the U.S. occupation authority. One person familiar with the deal said it took senior U.S. military and civilian officials in Baghdad by surprise. Because of the apparent lack of consultation, some officials said elements of the agreement, particularly the speedy troop withdrawal, may be tempered by the Pentagon or by the U.S. Central Command, which is in charge of operations in Iraq.
Sounds to me like Conway was doing all of this himself, but as your link points out, not all of the Marines liked it.
“The deal” is the eventual resolution of the cease fire with the Fallujah Brigade, not the "impostion" of ceasefire that restricted their operations for a month, and Bush eventually confirmed would stay in effect. That’s all I’m arguing was not the Marines’ choice.