So, the actual answer is that rings are collisional, and the parts of the ring at different distances from the planet will precess¹ at different rates if there any asymmetries between the planet and the ring, so the parts of the ring will keep moving slightly differently and bumping into each other until they settle into circular² orbit around the equater, where the symmetry means there's no differential precession.

¹err, wobble

²excelt moins can make non-circular, 'cause they break the symmetry