ORIGINAL: gkaraolides
What WEDJ said, plus the anhedral stab in knife edge counteracts the tendency to roll out of knife edge. This tendency is caused by 1. the wing dihedral and 2. most of the fuselage side area being above the centre of mass.
Also, there did exist a Curare without an anhedral stab. The Prettner designs previous to the Curare were the Sicroly series. The last of those, the Super Sicroly 2, was pretty much a Curare without the anhedral stab, and the stab placed lower on the fuselage. Hanno Prettner won the '75 TOC with the the Super Sicroly 2, before winning 2nd place in the '75 World Champs, 1st place in the '76 TOC and 1st place in the '77 World Champs with the Curare.
G.
If one prefers an aft CG, be careful with anhedral stabs. Aft CG and cross wind will cause all kinds of headaches on the anhedral stabbed model. The pitch up in S&L flight (stab forced down) is very weird and noticeable by even casual observers. My latest design uses the geometry and I really hate the model's cross wind flight character. Had to move the CG fore to about 25% static margin and it barely holds its own
The anhedral stab is supposed to assist model lock in all attitudes during rollers and such. In my experience it really didn't help these maneuvers.
The anhedral stab does not counteract any tendency of the wing to roll out in knife edge, unless the dihedral angle of the wing was incorrect in the first place. Get the wing's dihedral correct and you don't have to worry about your model rolling out in knife flight.
The anhedral stab adds vertical volume to the tail so directional effectiveness is ever so slightly improved. But if one wants directional stability, simply add fin area. Simpler and easier to get exact