The AMA does not approve or disapprove fields. They don't have a field supervision team going around the country making sure clubs build the fields to specifications. The AMA sanctions clubs, and provides guidance on how to build fields. They do not sanction or approve fields.

You can read the AMA's safety code. There you will find the information you are looking for. Basically as long as you follow the AMA's rules the insurance will cover you. The main thing on this discussion is that you need permission to the flying at that field / park. Either public or private. Check on local ordinances as some cities / counties have specific regulations regarding RC in public parks.

Rafael