Actually, the concepts of "blackness" and "whiteness" have been re-defined and contested throughout US history.Who gives us the 'right' to judge if some one is 'black enough' to be considered BLACK? or Irish enough? or Chinese enough?
The US concept of race has been a social construction, not a scientific one. For example, a person who can pass for white is almost certainly mostly European in their DNA, yet, a few "drops" of African blood often deems such persons "black"... it is society which constructs these distinctions. The distinctions being made have varied over time and space, and even within ethnic groups.
Regarding the subject at hand, if a person who enlisted identified themselves as white, and was assumed by his peers to be white, then that person should be considered white, IMO. There is such as thing as a white person with some African ancestry, as I see it, although this is not a controversy free notion.