Brigadier General Mark Kimmitt was asked about reports (mentioned by Schramm here) that an Iraqi army battalion refused to fight in Fallujah. He did not provide much clarity on why that particular unit did not fight, but he did reemphasize that two ICDC battalions fought side-by-side with the Coalition in Fallujah.
As for the non-performing unit, Gen. Kimmitt emphasized that it will take time to get the army units fully prepared to fight. My Monday morning quarterbacking suggests that this problem is exacerbated because the units have the Coalition to fall back on. It is easier to to dodge the bullet if there is someone there to take it for you. This is not a statement in favor of reducing Coalition forces, but rather an observation. The Coalition is increasingly integrating Iraqi security forces into their operations, so hopefully the "no go" response of this unit will in short order prove anomalous.