I talked to Doug Dix about this subject about a week ago. He said the only reason this pairing got started was because the first book to come out on the subject of uromastyx care said that it was acceptable to keep the two species together, and that in fact it is not a very good idea.
First of all, I wouldn't house anything with a male bearded dragon. They are completely belligerent towards any tankmates including females of their own species. Housing a male of each species together would definitely lead to aggression from the male bearded dragon. Housing a male bearded dragon with a female uromastyx could lead to attempts at mating. I have even heard of male bearded dragons poking their eyes out on the spiky tail of the uromastyx attempting to breed with them.
You probably could get away with housing a uromastyx with a female bearded dragon in the sense that they would not hurt each other. However, I would still not recommend it due to the fact that bearded dragons are known to carry parasites very often. Since the two species are from different parts of the world, something that is not very harmful to a bearded dragon could be detrimental to a uromastyx. I wouldn't recommend mixing the two at all though I see it done in the pet stores all the time.
Hope I helped
--Jeremy Miller