JR-
Why does AMA control the terms of coverage if it is not an insurance company?
By "terms of coverage," I refer specifically to the AMA Safety Code, which must be complied with as a condition of coverage, and which is controlled by AMA rather the entity that you recognize as an insurance company.
Frankly, I think the 'not an insurance company' argument is quibbling over semantics. The SIR is $250K, so claims up to that amount are backed by AMA reserves. Without having actual claims data available, I strongly suspect that the vast majority of them are for amounts below that threshold. In those cases AMA judges the merits of the claims and decides whether to pay or not.
I think it even the consensus of the EC is that most members join AMA for the insurance, either because they think they need it or somebody else requires that they have it before granting them access to flying sites.
Without the insurance business, AMA would probably fold.
What then is lacking from AMA's business that makes it not an insurance company?

Abel