ORIGINAL: mesae
An engineer once told me that the anhedral on the F-4 tail was to help with low-speed yaw stability. The tail of the F-4, like most airplanes, generates negative lift, so anhedral on the horizontal tail would actually work like dihedral for a wing (it's stabilizing). This seems to imply there is a tradeoff with yaw stability while inverted, which of course wouldn't be a problem for the F-4.
That is correct from what I remember my father (who helped design the aircraft) telling me.