Hearts and minds
I posted a while back on one of these surveys showing how most of the Iraqis are forming their opinions on something other than personal experience. Primarily via the Arab media, like al-Jazeera.
Al Jazeera and others like it would be feeding them anti-American crap regardless of what the facts were or what the military's behavior was. And what they can't find, they make up.
I think one of the biggest mistakes we made was not getting our own major media feeds in there a year ago. Some of this is being done now, but it's a little late.