I mean, something more than the thin smear of dust that it turns out Rhea probably doesn’t have anyway. Does the dance between moons and planets make it such that it’s no coincidence that no moons have rings, i.e., is it basically impossible?
The argument that the much more massive planet would destroy any ring system would also seem to apply to say a much more massive star would destroy any planetary ring system, but we know those exist.
However, I’d think that the moon would have to be quite distant from the planet to keep it. I believe the disruption would be due disturbances of other moons (so assume we have none of those) or to tidal forces which are proportional to the mass and inversely proportional to the distance. Since Saturn has 2 millionths of the mass of the sun and is 1.4 billion km from the sun, I’d think a moon around a planet the size of Saturn might be able to keep a ring system if the moon was about 20 million km from the planet. Saturn does have moons in orbits that distant, but they are all tiny.
Discrete planetary rings are formed by resonances between the primary and other moons which prevent (a least for some period of time) the material from either coalescing or being ejected from the system. So, it is unlikely that a moon could form rings unless it is large enough to have significant size subaltern moons of its own, or that they would be stable for very long.
Stranger
What this answer immediately brings to mind is, have we ever seen a moon with subaltern moons of its own?
No, and they’d probably be quite rare, but there’s no inherent reason they’d be impossible.
Alternately, you could have a transient ring without shepherd moons, but we’d have to be pretty lucky to find one before it dissipated.