There is no "race" gene in DNA.
What they actually do is identify DNA traits that are common in isolated cultural groups. It doesn't mean that other groups don't possess these same genes, just that it's more common in some groups more than others.
For example. Let's say a tribe in Arkansas got separated from civilization and had a cultural norm of chopping off the right hand as a punishment. Over several generations the group develops a left-handed society, before eventually breaking out of their bubble to spread out their genes all over the world. Then some scientist further in the future sees a left-handed person in Texas and concludes that's it's very likely that he had ancestors from Arkansas. It's not a very conclusive science.
http://nypost.com/2010/07/21/blond-bombshell/
Dispel the myth that black parents can't have a white baby. It's happened quite a few times. If the genes are present, it can be passed on. Dominant genes just have better odds of being passed on.