I'm starting to fear getting into music theory arguments, but I have something to say: You are both right.

First of all, in written music, the little signs by the notes to denote sharps or flats or natural notes are called accidentals, so cryptic is definately right on that one.

But also, (especially in jazz, where disharmonic notes are played frequently) notes played that are not in the key are also frequently called "accidental" notes. It could be that it's slang, but in class, when analysing jazz solos, my lecturer often calls notes outside of the scale accidentals.

There is seriously no point in getting into an argument over this though.