Pizza and pasta, the debates rage on. It's true that Marco Polo brought pasta back with him from China and introduced it to the northern Italians. At the time of this introduction the people of southern Italy had been enjoying pasta for decades (at least). This pasta took a form similar to what we think of as lasagna, in that it was sheets of dough rolled thin and usually baked. Food historians link the origin of this pasta as being Greek phyllo dough.
The origin of pizza is a long and tangled web (that not suprisingly leads us back to Greece). Some food historians trace the original pizza back to a greek dish of bread baked in round pans with an egg or cream-based sauce topped with cheese (Feta usually), and other relishes. While this lacks the gooey nature of mozzarela, or the tomato sauce that we have come to equate with pizza, few can scoff at the similarity. The Italians had focaccia, which they often topped with herbs, olive oil, a wide variety of cheeses and other savory items long before the introduction of the tomato from the New World. Many believe this to be the ancestor of Italian pizza. When the tomato was introduced from the new world, the Italians were one of the first to truly embrace the capabilities of this noble fruit. It soon became an key ingredient, a staple food, even, to many Italian dishes and I can't doubt that some ancestor of the modern "pizza" was one of them.
Food origins are complex things, and it's hard to say, "X dish comes from X country." As nations conquered other nations, and as people traveled the globe, the face of dietary trends changed with them. "Curry" was not an Indian dish, but an attempt by the Indian population to recreate a blend of spices typically used in Indian cooking so that the English occupying India at the time could take that flavor home with them.
The roots of classic French cuisine come from a French prince being wed to an Italian princess who insisted that her chefs come with her (after being unable, or more likely, unwilling to eat the food served by the native French chefs at the time), the Italian chefs taught the local French chefs what they knew of standard Italian cuisine, and in turn the French adapted and refined these techniques while sharing French culinary techniques with their Italian counterparts. Italian cuisine was influenced from all over the Roman Empire as slaves were brought back to Rome to prepare meals for their conquerers. Similar truths exist between Japan, China, Mongolia and Korea (before its 1950s split into North Korea and South Korea, anyway).
America brought about all new culinary puzzles as immigrants from many lands came together and fused traditional recipes with local ingredients into unique creations that are truly "American," or more technically, a creole of all major culinary schools extant at the time of mass emigration to the Americas.
All in all I feel these debates over the origins of food serve us little (unless you're a food historian or nutritional anthropologist). Some of the great resturaunts of our time come from the "fusion" school of thinking, bringing together the flavors and techniques from around the globe and creating truly international cuisine. Food may reveal a lot about our past, but it's nice to think about what it could say about our future.