To apply that to America, no one who comes to America and looks back to where they came is fit to call themselves an American.
Anyone who hyphenates their American Status is not fit to be called an American.
As the son of immigrant parents from Russia I have often had to make the case to people that I was a US person by birth and by service. My brother was killed on Okinawa in WWII and I served on Leyte. I received a BS in Engineering from the most renowned public university. At one time I applied for a position with a then very important/strategic defense company. In one of my interviews I was questioned as to my loyalty to the US. The interviewer even asked if I or any member of my family had relatives in Russia and if so were there contacts still going on. I honestly answered that my mother was in touch with my deceased father’s brother. The interviewer shook his head as if that was a no-no. However I did end up getting hired and had a very successful career with the company. I very much agree with the proposition that to be a true US citizen one must be centered like my mother and brother and I were. I doubt that 5% of immigrants today be they from Asia, Far East or south of the Texas/Arizona border can vouch for such.