There's your solution. If the guys are not AMA members and are flying on public land with no coverage for the county then the "guy from the county" has exposed the county (that's you too, the taxpayer) to all sorts of liabilities. Give him another shot at getting them off county property. If he fails, go to his superiors or go pulblic.

As for non-members hating the AMA, I would suppose that maybe they hate organaization and rules even more. I want to do my thing regardless of how it effects others. They know they are causing a conflict and it sounds like they are doing it willfully.