The Greeks were pretty successful at establishing colonies in Asia Minor (Turkey and environs) and Italy, but it was the Macedonians under Alexander the Great that really conquered the most area around the Mediterranean.
(You might think it's a small point, distinguishing Greeks and Macedonians, but there are frequent calls for Macedonia to secede from Greece, and form its own nation. Plus la change and all that.)

Either way, Egypt wasn't the "home" of the Greeks.

Still, as a song lyric, I don't judge it by the same criteria as a history book, so I give it a pass. :^)