It would be a mistake to assume that the security forces and govt of Iraq are all a happy unified single organization. From what I've been hearing from officers recently back from Iraq and who where in positions to know while there, for elements of the official security forces to be that corrupt and that in cahoots with Shia militias, Sadr's people in particular, is not only plausible but a matter of course.

When talking about this incident today, either scenario of some group pulling off disguising themselves as police through theft/black market means or for real Iraqi police to have been involved seemed fully possible, with the latter probably a bit more likely.