well , well, well, you were RIGHT till your last paragraph......AMA Chartered clubs have insurance thru their membership, If the owner of the land requires it, the AMA, will give that landowner a certificate of insurance... but the coverage comes from the individual members... homeowners first.....
Your Membership to the AMA covers you WHEREVER you fly, as long it is legal to fly there and you adhere to the AMA's safety code.
THERE is ONLY 1 AMA field in the whole USA... that is in Muncie IN. The flying site beside the AMA headquarters that the AMA owns.
If your local park allows RC... AMA covers you...... If you fly in your back yard, AMA covers you,
If I were you, I would do some reading before you school others on "how the AMA's insurance works"