I have heard many times that such and such municipality requires AMA but I doubt it has been taken to test.
I pitched the AMA to the City of St. Louis Parks Department and they were thrilled of the idea that not only will it be insured by the AMA, but they were also a National Organization that stood behind it, so they decided to require it, mostly in part for the organization portion which they are used too from other National orgs like National Soccer Assoc's, National Little League Baseball Assoc's which insure and most importantly, organize at a National and sometimes State level.
Keep in mind that Municipalities and Parks Departments are also part of other National Municipalities and Parks Assoc's, so they are used to the drill. Hard to get anything disorganized past them.