Why is the Latin "Oedipus Rex" a mistranslation of the Greek title of Sophocles' play?

Sophocles play, "Oedipus Tyrranus", is often referred to
by the misleading Latin title "Oedipus Rex". The reason why this title is misleading has
to do with the difference between a "basileus," a legitimate hereditary monarch, and a
"tyrranos", a sole ruler given power by popular acclaim or by force. Until the very end
of the play, Oedipus is a tyrant of Thebes. His power is due not to any general form of
legal legitimacy, but popular acclaim. It is only at the very end of the play, when the
parentage of Oedipus is revealed, that we discover that, in fact, he was the legitmate
king, or basileus. Oedipus does not, howver, actually rule Thebes as basileus, because
immediately upon the discovery of his parentage, he blinds himself, resigns his
tyrantship, and leaves the city.