aviationluver
Your second answer could be used to describe a dihedral as well...correct? In other words, dihedrals help with roll stability in a slip condition, so, what would be the difference between the dihedral and anahedral other than looks?
Apologies in advance if this seems too complicated or 'nerdy', but there are some fairly complicated aerodynamics involved and simple explanations of complex problems often lead to wrong solutions!
"Roll stability" is too indefinite a term for me as there are three lateral aircraft motion modes and they all involve roll. Increasing dihedral of either the wing or the HTP will stabilise the spiral stability and destabilise the dutch roll - anhedral vice versa. From what I have read, in most cases one wants to improve the dutch roll, for which tail anhedral would be a possibility, but putting the special case of the F4 aside, it would probably be easier just to fit a yaw damper, so I think introducing lateral stability into this discussion is a bit of a red herring.
In the longitudinal case one needs to understand that the downwash behind the wing is not constant. It is a maximum near the wing wake, but above and below that the downwash falls the further away one gets.
So if the wake lies below the HTP (cruise AoA range) putting anhedral on the HTP will bring the outer part of the HTP into a larger downwash. At high AoA the wake will move upwards relative to the HTP and if it lies above it then anhedral will reduce the tail downwash.
So "Yer pays yer money and yer takes yer choice". GUESSING from what Croucher wrote, they might have been attacking a high AoA problem, possibly some sort of pitch-up near the stall, but that is a pure guess.