Thanks for the replies. What we are being told is that, because we occasionally fly point to,point within the US, even as a private flight, the crew earned a portion of their salary while in the US. Uncle Sam thinks he has a right to a portion of it, and due to a reciprocal tax treaty between our two countries, the interpretation is we need to record those legs, file the returns, and subsequently pay tax if applicable. They are also suggesting that time spent within the US while on training and attending relative courses or conventions is also countable.
I am really curious if anyone else has been advised to comply. Guess the next question arises, what happens if I ignore it!