Having served on a county government I offer this tid bit.

If the county allows you to use public property, they can not specify that you must be AMA or what ever. What they can do, is specify the requirements that you must meet to get a pass to use the property. For example, they can say you must show proof of insurance and it must have coverage of these liimits. If AMA meets the requirements then you are good to go. However, you may use any insurance that meets the requirements. Typically, AMA is the least expensive way. This prevents governments from favoring certain factions.

If you lease the property from the government as a sole lessor and user of the property, then you can make the rules anyway you want. That type of lease is the same as owning the property for the duration of the lease.