Therefore they should do the JAA PPL if they plan to fly in Europe.
Maybe, but then I wouldn't go to the USA to do the JAA course as what you get there is US training for UK prices - i.e. you pay more for the same training as someone else sat next to you, because you are on a JAA course and they are doing the FAA PPL, and your FI might be the same bloke! (not dissing FAA training as I actually reckon it is better than most of the JAA rubbish).
What some clever folks do is do the JAA ground exams in the UK, then go and do the FAA PPL. As soon as the FAA PPL is in their hand (2 minutes after the flight test) they then arrange to have a test the next day with a JAA examiner.
Although a school needs to be CAA approved to train for the JAA PPL, a CAA examiner DOES NOT need to examine from an approved school to carry out LICENSE CONVERSIONS.....