Their theory was that is was questionable whether it was an NTSB incident or not ("Incident means an occurrence other than an accident, associated with the operation of an aircraft, which affects or could affect the safety of operations."), and that it was better to leave any not-absolutely-required negative things off the application.

I felt otherwise. Delta cares about honesty. Personally, I felt it better to be more open than not. So I put it down.