I don't know how fruitful it proved, but my impression of Pisier's counterexample to a conjecture of Grothendieck (a Banach space on whose tensor square all reasonable cross-norms coincide) is that it was unexpected at the time. Perhaps Bill Johnson can correct me on this if I am mistaken? It certainly qualifies as ingenious, in my book.

(out of office right now, will add details later)