The Hamburg Steak came from Germany but the idea of shoving it between two slices of bread with some onions, mustard, and later some ketchup, is American.
Pizza originated in Italy but resembles nothing like the things you get in Chicago or New York City - and both claim theirs is the "REAL" pizza.
Apple tarts may have come from France, Germany and The Netherlands yet none of them have any resemblance to American creations such as deep dish dutch apple pie, not to mention cobblers, buckles, foldovers, dumps, and so on.
These are but a few examples of foods that were brought to America by immigrants, only to share them with their neighbors and end up having them altered.
Most of what Americans call "Chinese food" is another good example of this.
So there certainly IS such a thing as American food. Many Americans can't name anything because they've never been some place other than America and are suddenly deprived of what they suddenly realize is "American Food."
Let's start on the East Coast. New England Clam Chowder, Lobster, Crab cakes. Not to mention the aforementioned Pizza.
Then we swing down South where you'll find BBQ, Southern and Soul Food, not to mention Cajun and Creole style cuisines. Those don't exist anywhere else.
Going into the Southwest you have Tex-Mex - the original fusion cuisine - best known for its creation "Chili" which folks in Cincinnati are very fond of served over spaghetti noodles, topped with a mound of shredded cheddar cheese and maybe onions.
Further to the west you have tons of fusion cuisine. The dish "Chop Suey" originated from an anonymous Chinese railroad worker. The so-called Chinese Fortune Cookie also originated from California. Today, you need only look for a roaming food truck to see the future of American cuisine. How about a Torta made with Korean BBQ chicken and Kimchee? Or a Mu-shu Burrito?
And let's not forget the indigenous foods from the American continents:
* Maize / Corn
* Chili peppers
This melding of different foods and cultures happens all over the world. For instance, the Pizza Hut in Japan serves a pizza topped with roasted octopus, corn, sprinkled with bonito flakes and seaweed. It's actually pretty good - sort of like an Italian Cioppino spread on a pizza crust. But definitely not what you think of when you think of "American Pizza."