That's historically accurate actually, because "Greek" was not a race, it was more like a cultural identity that you could pick up by practice. A black Greek would just be a Greek with black skin. If they spoke Greek, worshiped the Greek gods, understood Greek cultural practices, lived in a polis, boom they're Greek.

I knew this was true of Romans, and it makes sense that it would be the same for the Hellenes, but still good to know! I think even among people who know and accept that "race" is a modern construct, it's hard to truly internalise that not only did these cultures not conceive of themselves in racialised terms, they were also more or less cosmopolitan.