It seems the reporters are "a twitter" of being verbally anti-gun or anti-people owning guns.
Seems to me that if people were more in "polite society" (ala Heinlein) mode, the looting would be less likely because the "citizens" would not be so certain the criminal element is the armed element.
Here's the problem too. Violent crime in NO is nothing new, it's just exacerbated because of the storm.
New Orleans is listed as the number 3 most stressful place in the US to live...reason "violent crime."
http://www.bestplaces.net/stress/stress_study1.asp
Not so sure about there being a direct correlation there. Based on their looting choices, the looters don't seem to be particularly capable of the sort of forward thinking that would cause them to be polite. If anything, they'd probably have armed sooner, and made sure to shoot first.
If I'm right, the only way the shooting becomes "less likely" is through attrition.
I really don't think the looters are civilized. They're more like jackals.