I was in Florida last 2 weeks ago and flew with an instructor on my JAA license (R22). I have previously done training over there on an M1 visa but this time was on holiday with a visa waiver. My M1 has expired.
I am looking at getting an FAA license and bought a copy of the FAR's, and read in detail the stuff about visa requirements because I wanted to do some night training to add to my log book and then use to get the FAA license.
My understanding was very clear, the <12500 rules written above by Skyhawk preclude you from PUT (Pilot Under Training). However you can do P1/S (Supervised) because that's not training that (as a pilot) you would put towards a rating. I didn't look at it from the perspective of whether my JAA license allowed me to act as P1 in a supervised role without applying for a permit to fly (wish I had now!), just whether I could do training.
I declined any night training because I was concerned that when I sent my logbook to FAA for validation in the future, they would tie up visa applications with PUT time and I might have an immigration block in the future for violating my Visa waiver status. I did do a couple of hours P1/S for fun and a general brush up of skills in the US.
The flying school was fine with renting me the a/c and the instructor for this. They were also prepared to do PUT night training after I made specific enquiries about its legalities, but I think they were wrong and stuck to my own FAR interpretation!
BW