[posterboy]

There is no single gene that determines skin coloration.

You are right insofar you allow yourself to be imprecise and make sweeping generalizations. Of course a light skinned person is far less likely than a person with darker complexion to have ancestry who lived ca. 2000 years ago in for example south africa, but there's a whole lot of leeway in those 2000 years and at the very least its ignorant of e.g. India. And then the question is whether the question mattersat all.