Here's how it looked to the UK schools sending students over :
Pre- 9/11 the students were told that they were going on a vacation/pleasure trip, and to say so (and nothing about training) at immigration. This did not require a visa for EU passport holders, and was the officially correct designation of non-FAA training in the US, as it had no official status of course.
Post- 9/11 the schools were arranging visas for students as a precaution.