Alfredo Nicoletti, son of the man who built the bicycle, was kind enough to respond to our email seeking information about the bicycle:
I'm Alfredo Nicoletti, excuse my terrible english.
The story of this bike (the first and the second) and the American student you know is correct, I remember it very well, my father made, I was 7 or 8!
The frame is out size (the boy was quite tall), year is 1960 or 1959, you are right: front wheel is not original and pedals and bell too, but it is a great bike.
I stopped building bikes two years ago, now I restore vintage bikes and collect Campagnolo parts, if you were in Italy I should be happy to set non original parts but I think it is complicated.
If you want to know something else about this bike ask me: I'll be happy to answer.