Well, let's be real, pizza isn't some kind of holy thing that is only Italian.

It's not like they're the only people to ever put things on flat dough and bake it.

But ignoring that, food is a living thing, just like most languages, like music, like fashion and art. You can try to stick a pin in it, but you kill the thing by doing so.

It reaches a point where it's ludicrous to try and claim a thing is possessed in its entirety by the place that first named something.

Once a cultural idea spreads far enough, you can only specify one type of the thing. It's why we have champagne, and sparkling wine. It's a way of putting a pin in something but recognizing that there's still living versions out there.

Or, look at it like the difference between formal and colloquial language.

Pizza may have started in Italy as a term, but it's like kleenex and qtips. Pizza is now the generic term for stuff cooked on flat dough. It can even be applied to stuff being placed on flat bread, and then cooked, though I don't know why you'd not call it one of the other words for that idea other than being unaware of those words.

Put whatever you want on your dough, call it pizza, and enjoy ;)