You don't need popular support if you have fear.
The insurgency has been terrorizing the population of Fallujah since last spring. Those who were left there to run the place were either coopted or killed. Abuse of the citizens was rampant.
People don't have to love you to do what you say if you carry a gun and have a tendency to behead people.
For that matter, this was also true in Vietnam. The Viet Cong did not use gifts and bonus points to control villages. Talk to a Vietnamese immigrant sometime.