Eowyn Destroys the Witch King

One of the most memorable lines from LOTR is when Eowyn kills the Witch King. "No man can kill me!" To which she replies "I am no man" and stabs him in the face. Later in reflecting on the incident, I wondered whether that actually worked because the prophecy was meant to be understood so literally, or whether the Witch King's confidence, at that moment, was so shaken that he became vulnerable to a new interpretation.