Brian,
I think you need to have another conversation with him. There are only 2 ways I know of to be covered by the AMA when the student is NOT an AMA member.

The first way is when it is a familiarization flight the instructor is giving to encourage someone to join our hobby. This is when you get to infect others with your approach to fun.

The second way is only good for 30 days and can only be done by a club appointed (and PAID for) AMA Introductory Pilot. He can train a student who has no AMA for 30 days, but I believe it has to be on HIS equipment rather than the students. Lots of paperwork and more questions than answers at the flying field, but it is approved.

Anything else is a risk being taken towards the instructors AMA secondary insurance coverage.