There is a fairly infamous anti-trust lawsuit that went to the Supreme Court in 1984. It had to do with two aspects of the Sherman anti-trust regulations, the first part which prevents competition and the second part which has to do with tying of services. Essentially the ruling at the Supreme court level was that an anesthesia practice could have an exclusive contract with the hospital as it did not violate this part of unfair marketshare and weeding out potential competition. (Google Jefferson Parrish Hospital v. Hyde).
I'm no longer sure this is the case.
With the explosion (and thats the only word) of AMCs and the decrease of competition for market pricing in particular healthcare markets, they may in fact now be violating the first part of the Sherman antitrust laws regardless of the tying aspects. It would be interesting to see if, say, an anesthesiologist who lives in an area and wants to work at a particular hospital with a particular set of surgeons who are unhappy with the crappy intra-op care their patients are tied to by having to deal with these AMCs could win such a case. (It is my understanding that this a similar model that already exists in the San Antonio area with particular anesthesiologists working with certain surgeons directly.)
I'm not saying this is the best solution or the most economically viable way to do things for individual anesthesiologists. It certainly would involve litigation and these AMCs have the resources and deep pockets to battle it. Also the current composition of the courts may not be favorable to such a challenge. But I'm suggesting that the way these big AMCs operate as relative oligopolies may present a unique legal avenue of recourse for anesthesiologists in anti-trust litigation. It all depends on what you're willing to fight for, I guess.