Well, I guess it's probably a bit daft to think of the food of countries like the US and UK (where centuries of immigration has changed the national diet so much) as having nationality. It's well known that French cuisine is derived from Italian cooking, more specifically from the recipes and techniques brought to France by the squadron of Italian cooks that Catherine Medici insisted on taking there once she'd realised how awful French food was 500+ years ago.
As Wiki points out in a section titled "Problems with defining American cuisine", "The cuisine of the Native Americans was of course the first American cooking style, and it lent a great deal not only to subsequent American cooking but also to culinary styles around the world. Turkey, corn (maize), beans, sunflowers, potatoes, peppers, and various forms of squash".
http://en.wikipedia.org/wiki/American_cuisine
I think I'll have roast beef, lamb or a steak and kidney pie thanks.
In any case, I really don't see how you can consider an adapted West African dish like gumbo to be any more American than, say, adapted Indian food is British.