I'm guessing it was done immediately after he was handed over. Why would they let the Iraqis get him early so he could escape? He's gone.
You're probably right-- personally, I thought the same thing when we "captured sadaam"-- I figured that meant "Sadaam has been shot in the head and pushed off the back of an aircraft carrier..." but I was wrong...
I don't think the US has actually handed them over-- if so, there's definitely US intel involved on the Iraqi side so as not to lose him... IMHO...