Is the stability of a stable ring system dependent upon the body having moons, maybe moons of at least a certain mass and orbital distance? That is, can you have a stable ring system but no moons?
I’m not capable of speaking of the physics of your question. However, a day or two ago we got news of an asteroid with rings. There was no mention of any moons around it.
Actually, something I read in the news of that discovery is what made me think of the question:
http://www.space.com/25225-asteroid-rings-discovery-video-images.html