I did look into this and confirmed that the visa story is an old one used, by UK flying clubs and US FAA part 141 schools, to frighten people off JAA training in the US. You do NOT need a visa for a vacation during which you are recreational flying (includes JAA PPL course)in the US unless you are doing FAA accredited training- isn't that unlikely or stupid if you are a Brit?
You are eligible for a visa waiver, just like any other European tourist, but the decision is always that of the officer at the port of entry. Is it any surprise that silly sods, who say they are student pilots or give the impression that they might want to work in the U.S., have created a problem for themselves, when there isn't one?