This whole passport cliffhanger may be a bit overblown.
Assuming the first leg in Russia is a NON-Elimination leg, the Rockers are still alive if they get their passport back.
sooooooo..... the simple thing to do is to get the police involved asap. The camera crew that follwed them that day has a video of their cab driver (blah blah insert legal stuff here). All they have to do is provide the police with a picture of the driver, and assuming all the licensed cabbies in Moscow are on file, do a quick check of the cab companies in town and locate the cab with the passport. This could take less than a day, more than enough time given the mandatory pit stop time. They could be good to go in time for the start of the next leg. (assuming everything goes smoothly) The key here is that the camera crew recorded his image.
Or something like that....