You mock the idea, but both happen more than you would think. About half American who have Black ancestry do not know they have Black ancestry. They are clustered in the South, and are often poorer. It is not uncommon for them to hold white supremacist views. Many Nazis had Polish and Jewish ancestry that they often did not know about. Sometimes they actually knew about it. Again, it was poor people looking for a step up in social status due to a supposed race.
We should not be surprised that racists lack a scientific basis for their racist beliefs.