One of the key components of sustainable power and influence is consistency. If people understand that you will keep your word and behave in a consistent manner, they will respect you, whether or not they like you or what you are doing. It is good to be loved; it is better to be respected.
Western Anbar is a place of tribes and extended families. Each group and sub-group has a reputation as do each of the sheiks. These groups are constantly vying for advantage and position. The Anbaris have come to see the Marines in terms they understand – as a tribe with a history and a reputation, although outside the tribal system. They have come to see the Marines as the toughest tribe in Anbar, the tribe with the longest memory and the one that will pay back in the terms used by the ancient Roman Lucius Cornelius Sulla (Felix) “No friend ever served me, and no enemy ever wronged me, whom I have not repaid in full.”(BTW – a good biography of Sulla is Sulla the Fortunate. It was published in 1927, but I don’t know of a newer one. You could also go back to Plutarch, which is available in full text translation on Google. Sorry, I can never resist the digression.) This is good. The Marines have won respect in Anbar in their own terms.
The Marines provide consistent security which allowed the flowering of Anbar we are now seeing. It is more than security from insurgents & AQI. The Marines also provide a kind of impartial and honest outside force that helps guarantee the regional tribes and grouping against each other in their sometimes violent competion. It is a smaller scale version of how the U.S. & NATO allowed the French and Germans to give up their ancient suspicions and hatreds since the security of an outside force eliminated incentives to stealthily surpass and surprise your opponent with a sudden, devastating, power. The potential down side of what amounts to a hegemonic relationship is that it can break down if the outside force weakens or disappears before the embers of the ancient hatred and suspicion are gone. With any luck, the people get to like working together better than destructive confrontation. It worked maybe too well with the French & Germans.
This interrelationship would be an interesting subject for an anthropologist to study. People always understand new development in their own terms and try to make sense of them in relation to existing structures. It is not surprising that the Anbaris would see the Marines as the toughest tribe in Anbar.