The point is that Germans are not in the habit of classifying people by race unless they're racist, and even then they don't tend to think in terms of Whites vs Blacks. For Nazis, it's about Aryans vs Jews, where the "Aryan race" is considered to consist of tall, blond, blue-eyed people. Most Greeks would not be considered Aryan, as would most Germans, for that matter.

I find it quite telling that you are surprised Greeks might be considered anything but white, while not showing any surprise about Turks. I don't think there's any difference in skin color, so that confirms my suspicion that "whiteness" isn't just about looks.