That is absolutely correct. My wife had an ancestry search done by her daughter and found she had a black ancestor in her lineage from several hundred years back in England.
So I (jokingly) asked her if she wants to claim some sort of affirmative action benefit. We have no idea what kind, but there's no harm in trying. lol
The problem here is that genealogical research is full of inaccuracies. To take just the most obvious one, it assumes the biological father of every child is the husband.
That’s just not likely, when you’re talking about hundreds or thousands of ancestors.
DNA, however, doesn’t lie. It tells you that you have certain genes associated with specific groups, but generally provides you with no way to figure out when and where the gene got in.