Suppose that the non-AMA member sets up a chair and some unsuspecting wife of a member trips over it and breaks her back. She sues the landlord, and the club for neglience. The landlord is covered, the club is not. If there is a judgement, you, as a club member must shell out. Forget whether it is fair, the tort system makes it possible. Are you willing to put everything you own on the line to let a non-AMA member fly? Most clubs answer with a resounding NO.
Someone being hurt at a club field, ie step in a hole, fall out of a chair, etc, spectator or... is a lot different than a non member flying at the site and hurting someone, etc. The claim would have to based on the person doing something allowed at the club property. Someone couldn't come on the property with 2 cars, play demolition derby on purpose, then put a claim against the ama since it was on a club field!!! A spectator setting in a chair watching (is invited by the club) and having a mishap I can understand being covered. A non member flying (not given permission by the club) and having an accident has no basesa for a claim as they were doing something not allowed!! I have a very hard time believing that the ama would cover this.