Assuming that you're referring to the AMA here, their role is pretty unclear to me. They appear to have played a lobbying role to get Congress to freeze residency funding in 1997 to avoid having lots of doctors [1], but for several years now, the AMA has at least publicly claimed that they've been lobbying congress to increase funding for residency slots [2]. Maybe they're lying? But I for one don't actually know who is keeping residency funding low.
[1] https://qz.com/1676207/the-us-is-on-the-verge-of-a-devastati...
[2] https://www.ama-assn.org/press-center/press-releases/ama-bui...