The Greek royal family are actually Danes. Their family name is Schleswig-Holstein-Sonderburg-Glücksburg. They were invited to take the throne of Greece in the 1860s. The first one was George I, a younger son of Christian IX of Denmark. The SHSGs intermarried with German and Russian royalty. So he has not a drop of actual Greek blood.
Thank you, La Lydia! Proven right again!