My comment was related to the fact that there actually is "something", call it terroir, call it local knowledge or whatever that makes those products different, no matter how hard you try to reproduce them outside (and no, it's not nostalgia, people I know who are not even Italian have the same opinion).

For what regards the rule, the main reason it exists is to protect local businesses I think. Many of these productions are local and small. If someone big from US or China comes with a product of the same name the industry where the product was created is lost forever.