This is a point which I tend to find puzzling and amusing. I frequently get asked what part of Scotland I'm from, or my family is from. Folks see a large, ruddy faced, bearded guy kilted and playing the pipes, and make the automatic assumption. I explain that my father was an avid genealogist, and that the earliest Young (family name) he found he believed came from the Kincardineshire region of Scotland, but he was unable to get firm proof. However, we do have the record that shows he was married in Phila. PA in 1742, so by my estimation, that makes me an American.
Just the other day I was speaking about "hyphenated Americans" to three of my grandkids. I sit (stand and sometimes run) at the head of a decidedly interracial family. I'm of European stock and my wife is Japanese. Our youngest daughter married a black man. I picked up her three youngest kids from school to have dinner with us. On the way home the conversation turned to ?/Americans. I explained to the kids that their grandmother is a Japanese/American because she was born in Japan, and became an American citizen, but in my opinion, anyone born in this country is simply an American. We all have different ancestry, but we're Americans.
My granddaughter seemed a bit disappointed that she was just a "plain American", but her brothers seemed to take to the idea better.