I mean, the same question can be turned around: When a ***-American who grew up elsewhere can't read or write English, are they still considered a "true" American, and is it racist to say no?

BTW, have you heard that rumor that genetics testing showed that Genghis Khan was genetically related to 刘邦? I have no idea if that's true or not. But certainly, during the 魏晋南北朝 period, there was a 匈奴汉 faction whose leader was descended from the "princess" married off from the Han Dynasty to the 匈奴, and thus can claim relation to Han royalty. :p

Also, just to note, your TLDR is a little long for a TLDR. XD