Oh, goody... a philosophical discussion! Since all but the "native American" came from other places and historical studies indicate that even they came from someplace else, there can never be a ethnic American based on original route philosophy. I say hogwash.
Humanity didn't just start to pop up in random areas across the globe like Dandilions on the front lawn. It all had to start from someplace so I will leave that determination up to each individual belief, or in simpler terms, whatever floats your boat. Everyone started someplace. Ethnicity is a defining of culture and tradition. It only matters where you were actually born. For example, My X's Father was born in England and spent his first five years there. He was, technically English. His Daughter was born and raised in Canada. She never was anywhere else until she was over 21 years old. She is not English (she does have an English Father) but, she is Canadian, ethnically! I am a mixture of French, German and American Indian... I am none of those things, I am ethnically American and it does not matter one little snip where my ancestors are from, that is just the route that was taken to get here.
Years ago, when immigration was at it's highest, people from the other nations tended to accumulate in set areas, be they Italian, English, French, German, etc. because that was where the people that they could identify with were located. It made a difference because then they could gradually transition without losing their heritage, language and culture. People at that time got in the habit of calling themselves by their originating home because they were proud of it and they didn't really know, yet, how they fit in with their new culture.
The last three generations of my family were all born on United States soil. It doesn't matter where their parents came from we were all American Culture by then, and therefore Ethnically American. We just, for some reason, have a tough time accepting that. I'm not sure how many more generations it is going to take before we all feel comfortable with being just plain American, but, it should happen before too long, I would think.