Definitely. But the sentiment these days are that the immigrants are natives. So therefore the food that is made is native too, by extending the logic.

There comes a time where the imported variant becomes more popular than the original. Just look at the italians and pasta.

The Americans rightly claim a lot of food that was made similar elsewhere, but garnered popularity in the us. Hamburg-er is a perfect example. They also “claim” food that might not necessarily be considered American by everyone, like pizza.