Very likely to be true and I wont disagree! I'm not actually even from the US so I'm unfamiliar with their scope. I disagree with the person I'm replying tos reasoning more than anything. Their objection was of a different nature than yours.
You're right, it isn't a union, it's a cartel!
No, a cartel is a group of competing firms in the same industry that form an alliance.
The best analogy for the AMA would be something like a guild.