Typically the state can require AMA, UNTIL SOMEONE CHAlLENGES IT. I am no lawyer, but typically a state cannot require membership in a private organization, even if the intent is to have one specific form of insurance, to utilize a public resource.
I imagine, that if really pushed, they would have to let someone fly without any specific insurance coverage since no special club memberships or insurance are required for other park uses.
I know of two situations where public land is used for RC. One was in St. Louis when I was there, called Buder Park. It was owned by the county and rquired that you obtain a field use permit. Part of the application was proof of insurance, I had AMA so I used that, but I don't recall if it was specifically required.
The other instance is in Omaha. There is a club that uses a public park. In that case, proof of insurance was required, but it did not have to be AMA. Additionally, you didn't have to be a member of the local club to fly there.
I would also ask the ranger where in the state law it specifically states that AMA insurance is required.
On the bright side, at least you may still be able to fly there, in my state, RC is specifically prohibited in state parks.[

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