I agree that sloppy data collection accounts for a portion of cases. It may well be, as you suggest, the predominant reason. However, my impression, which I concede is not a validated instrument, suggests that 1) incidence rate of inter-racial relationships resulting in offspring has been increasing substantially over recent decades and 2) referring to oneself as multi-racial rather than choosing one, is becoming more common.
Looking at recent news-
In the US, in recent times, a person with one parent of African ancestry and another of European ancestry, would, typically, be referred to as "Black", unless their complexion was so light that they might "pass for white", in which case they might choose that label.
Recently, the actress Meghan Markle of the US and Prince Harry of the UK announced their engagement to wed. Ms. Markle's parents are of disparate race. In the press accounts with which my eyes have been bombarded, it seems that she is more frequently referred to as being "bi-racial" than "black".
Conventions are evolving. How OMOP should address this, I don't know.
I suppose that we could have a one : many relationship from person to a new table RACE. But that would seem way more additional overhead than would be reasonable, and would then raise additional questions such as: should a person's list of races be ordered? Do we have parallel options for people who refer to themselves as multi-racial and for those who are explicit in how they self-categorize?