I don't think its true that they're allowed to increase the cap. These quotes suggest otherwise.
"Physicians and medical students from across the country are urging Congress...to lift the cap on the number of available residency slots." http://www.ama-assn.org/ama/pub/news/news/2013-02-03-urge-co...
"The BBA resident limits have imposed significant limitations on the ability of teaching hospitals and medical schools that sponsor and conduct graduate medical education programs to respond to the needs of the communities they serve." https://www.aamc.org/advocacy/gme/71178/gme_gme0012.html