Yes but I have been on company training courses under the visa waiver and that is allowed - stamped in as B1 - and INS had no issues with this.
Theoretically to do an approved course, for which the Visa was issued, it'd have to be under pt 141. As you say, most are not anyway, and therefore you are probably not doing the course under the terms of the visa. Many flight schools who are not Pt 141 use their "mates" school to do the visa stuff and then they come to the pt 61 school on arrival. It is all a paperwork game and a waste of time getting worried about.
Anyway, I don't really care. If I really did want to "steal an american's job" (which I was accused of once by an INS official) or remain illegally, I'd just apply for a green card
