You could fly as PUT with an instructor BUT this will also require an M1 visa
Sorry, CZ, but that is not correct. You are able to fly with an instructor, and log the time as PUT, on a Visa Waiver, so long as you are not training for a license or rating. Club checkouts, BFRs, and just flying around for a bit of fun are all ok. Training for a PPL, IMC, IR, CPL and so on, however, will require an M1 Visa. That is assuming that you are entitled to enter the country on a Visa Waiver in the first place, of course. And remember that the only thing which really counts is the way the person working the immigration desk on the day you arrive interprets the rules..... if he decides to send you home, it makes no difference what the law says, you're going home and you don't have any right to appeal.
FFF
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