In this country of immigrants, a white person can be an immigrant, a non-white person can be a natural born American.
A couple of months ago, at our dinner table, Justin told us a traffic accident involving his friend's family. He refereed to the other driver in the accident as "American". "Do you mean the other driver is a white person?", I asked. "Yes", he replied. "You know", I said, "A white person can be an immigrant. You are born here, you are natural born American ...". He then explained that he refereed to the other driver "American" because his friend's mom did so.
A couple of weeks ago, a co-work, who is originally from Asia, refereed to a white co-work as "American" when he talked to me. I did not stop him this time because I did not know if he is an American or not.
In fact, some Asian-Americans still refer to white people as "Americans" during casual conversations. This might be partly due to the fact they had been foreigners for so long before naturalization. On the other hand, this behavior may indicate a deeper issue, that is these Asian Americans still subconsciously treat themselves as "foreigners" to USA!
Of course, it is U.S. citizenship that determines a person being American, not the color of skin. For naturalized citizens, it will take more than a citizenship for us to establish our American identity.
A key to our American identity is a conviction that we belong to this country and the country is our country. To belong to is to participate in political process (vote in elections, run for offices if personally inclined to....) and to participate in criminal justice process (obey laws, report to jury duty...). To belong to is to get involved in the communities we live in. To belong to is to be a part of it, to assimilate into the main stream cultures.
When we truly feel that we belong to, we are truely citizens of the country.
Back to the dinner table, Justin said that we were refereed to as Chinese, Asian all the time by white people. I told him, it is OK to be refereed to per our race or ethnic background. When this occurs in a conversation, we refer to other people by their race or ethnic background as well - black, white, Hispanic, Caucasian..... When citizenship is refereed to, we proudly say "We are Americans" because we are.