Doesn't the AMA serve the medical industry? They don't have to make profits themselves. If a byzantine coding process raises medical treatment costs, they'll do it. Just like how they intentionally cap med school admissions to keep doctors in demand and inflate their salaries.
Any non-profit can always claim to inflate their expenditures up to (and above) their expenses and pay lavish bonuses to their employees, like you said.
Doesn't change what it basically is - aka Scamming the Public, and privatising the gains.