> They exert enough influence over all fifty states and the various private institutions to systemically deny training to qualified candidates?

Yes. What’s difficult to believe about this? People respond to incentives. The incentive for every physician is to maintain a shortage of physicians, therefore improving the job security and earning potential of every physician. The only way this could be done is if the physicians formed some sort of cartel that could control how many people were allowed to become physicians. This is what the AMA is and what it verifiably does.