I read Anderson book about anhedral in big airplanes- there was nothing about wingtips and CG, instead, as a jet powered cargo plane has a swept back wing, the anhedral is used to decrease lateral stability. There is not much, if any, anhedral in prop driven high wing planes, which usually doesn't have swept back wings. Anhedral is to cancel the effect of swept back wing on lateral stability, as LouW excellently described above.

And position of CG in respect to aerodynamic center (or neutral point) does matter- Dick should fly those extreme planes with pusher prop to prove opposite!
Normal, orthodox, designed in the box planes have no problems of using pusher props. Being heavy and without excess of power. And they still fly.