If the instructor is in the RHS to go for a jolly and get his hours up under the FAA system and does not in anyway instruct you then you would log P1 under JAA and he would log whatever they do in the US. I did 100 hours out in the US and became Mr Popularity as FAA instructors with time on their hands would want to come for a ride and enjoy a nice sleep whilst logging hours. Nice work if you can get it!
I see your point. But if you fly with an instuctor, and you know he's going to log P1, then surely you can't log P1 under our rules. Only one of you can be ultimately responsible for the flight. If you'd busted a TRA, which one of you would have wound up in court?