So seeing as Washington was a Virginian, he shouldn't be the leader of the Americans, right?
Arguing that a leader from a sub unit of a particular culture shouldnt be the leader culture is pretty dumb; if you trying to say that Alexander wasn't* Greek, then you would be mistaken. Modern Macedonia has no relation to ancient Macedonia; the modern state is a slavic splinter of the former Yugoslavia; ancient Macedon was a somewhat back water but still very much Greek nation of the Dorian branch of the Greek family.
*edited for proper spelling, as later quotes show