The AMA might not control it directly, but like any good union, they are politically active and have members on the relevant controlling bodies...
https://www.forbes.com/2009/08/25/american-medical-associati...
https://www.motherjones.com/kevin-drum/2013/11/its-doctors-w...
When both Forbes and MotherJones can agree on something (maybe this is the only thing :) ), there must be some truth to it.