I doubt Bud light cares about sponsoring any other MMA and even if they did I expect they'd be in a better position to avoid this kind of pressure. For the shirt companies challnging the UFC would obviously be a very risky tactic, they'd potentially lose by far the largest advertising market. Again I'm not going to say this could definately be challanged sucessfully(espeically with Zuffa's legal muscle) but to claim its the "basic rules of free exchange" is to ignore that there is a great deal of legislation protecting agenst monopolistic pratices similar to this.
Well I would need to see the existing contract, if there is one, rather than a per fight agreement, but the point remains, they are free to sponsor whoever they want, and the UFC is free to allow or not allow any sponser they want, for any reason. Why shouldn't a business be able to determine who gets publicity based on the business product?
It isn't a monopolistic practice though, they aren't doing anything to effect other MMA orgs, which is their competition. They are simply controlling who wears what in their show; same as all major sports leagues do.
I don't believe they'd need to be effecting other orgs for this to be an issue although cutting out sponsorship for fighters could obviosuly effect then indirectly, less sponsorship means they have to pay their fighters more to compete. Plus of course we had the same kind of thing rumoured for Afflictions Vegas show, Zuffa supposidly telling anyone who delt with them they would no longer be getting UFC business. Monaro clearly has no impartiality on the subject at all but I think its pretty clear that Zuffa is a company that likes to use strong arm tactics of questionable legality, just look at the whole mess with xyience which has a number of lawsuits attached to it last I heard.
If they aren't interfering with other organizations, then it can't really be pursued as a monopoly case, because they aren't in the sponsoring business, they are in the fight organization business. It is not an uncommon practice in the world of sports.