You got that right. Putin is parading it. I would not rule out that Putin is cooperating Bush under the surface, pretending to be a Saddam's friend, but keeping close taps with Iraqi situation, sometimes working discreetly to influence the mood inside Saddam's regime. Some may think this is far fetched. But I think that Russians in Iraq now can be a Trojan horse for upcoming operation. Or at least that is on the table for bargaining. It will be decided by whether Putin is satisfied with what Bush can offer in return.
Putin has no reason to stick to Saddam if Bush can make a better offer.