If I've heard the recording of the eventual departures of MS986 and LH411 from JFK correctly, the MS crew was given the phone number to call and the reason ("possible pilot deviation") immediately prior to taxi for departure. This sounds to me more like a doctor hearing while scrubbing up, over the hospital PA system, that the state medical board would like him to call about "possible malpractice" after he completes the upcoming brain surgery. I'm sure the MS crew knew they were going to have some questions to answer but being "called out" in so public a fashion just prior to takeoff certainly doesn't seem like the best way to handle it. Perhaps there's a legal reason to do so, but no flight safety reason I can come up with.