One of the first question that comes to my mind in such stories, when an organization goes off the rails, has to do with the governance structure. How are policy statements developed and adopted? Who actually calls the shots? There are many organizations where the nominal members have long since lost any effective control. If members are free to leave, that's not a serious problem. But if the organization has insinuated itself into professional training and credentialing, it becomes a problem. If the organization becomes a gatekeeper, control over the machinery matters a great deal.
The AMA has no authority over med schools certifications, no authority over licensing physicians or certification. It is strictly for lobbying Congress on behalf of physicians. But over 90% of their operating costs come from the US Taxpayer.