Well that just confirms she's not from Naples. There are Italians that eat pizza with ketchup because little known fact, Italians are fucking obsessed with ketchup. It's the second most bought sauce after mayo. Apparently it's used as a dipping sauce for chips. When someone mentions they eat their pizza with ketchup, they usually mean they dip their pizza crust in ketchup. So no, she doesn't lose her Italian citizenship by eating pizza with ketchup. However, if she eats pasta with ketchup, the local village people lynch her.
EDIT: Also worth mentioning, the "eating pizza crust with ketchup" isn't done at restaurants, it's something people do at home. It's like mormons and drinking.