The scooter was produced from 1944 so it actually wasn't even used in Italy. I had in-laws living in Italy during WWII. They weren't buying any scooters, just trying to stay alive. I don't think that afterwards that they would have been interested in an advertisement for a product used by the military force that invaded Italy, defeated them, and bombed the crap out of their country.

I'm not saying that the Vespas development wasn't influenced by the Cushman, it's just that it didn't happen the way you said it did.

https://www.warhistoryonline.com/instant-articles/the-history-of-the-cushman.html?chrome=1