"I thought it was implied (or maybe stated) in the AMA insurance stuff, that if an AMA member flies a model at a non-AMA designated field, he is not covered by AMA insurance....."

Im fairly sure that you are covered by the AMA wherever you decide to fly. The problem is that the owner of the flying site is not covered.

Example. The property my club flies from is owned by the city and the city is covered through our club charter with the AMA. If the club were to let the charter lapse the city would shut us down until the charter was renewed and therefore providing the city with some level of insurance. Your/My club may also add additional flying sites to the charter for an additional fee per year.

So flying out in the middle of no where with nothing or no one to harm in site, I say go for it. Flying off someone's private property I say be extremely carefull as they can be liable for damages also.

Cheers.
James