Under Italian law, if any of Rudy's grandparents had children in America before they renounced their Italian citizenship and became American citizens, Italian citizenship passed to their children and to Rudy, unless any of them walked into an Italian consulate and renounced it.
I'm in the same boat, but another generation removed. Both of my parents were born here. All four of my grandparents were born here, but one grandfather was born before his father renounced his Italian citizenship. Under Italian law, I am a Italian citizen. If I hassle with a bunch of paperwork to prove that line of descent, I can get an Italian passport. Am I a "natural born citizen" of the US?
It is my understanding that you are a natural born citizen because your parents were bone here and you in turn were born here. :)