I spoke with a friend who worked aero on the F-4 series of airplanes. He said the anhedral tail was an attempt to position the tail in a favorable position relative to the wing downwash, with flaps down, when landing on an aircraft carrier.

I remember a series of magazine articles by Don Lowe that discussed the horizontal tail's vertical position and its effects on a pattern model. I think I remember the pitch in knife edge could be controlled with position on the fuselage. In general he recommended a low position for best flying. With the Curare the anhedral achieves the same result while allowing the root of the tail to be higher. It would be just as good with the tail lowered a inch or so. It certainly looks business like with the anhedral tail though.