Everything in the Solar system is gravitationally bound by the Sun, which is what makes it part of the system in the first place. In that sense, yes, and really

Everything in the Solar system is gravitationally bound by the Sun, which is what makes it part of the system in the first place. In that sense, yes, and really the whole Solar system is too. There’s some nuance lost in that formulation though, because unlike a moon that came too close to its planet, broke apart and became a ring, the asteroid belt is much more distant and diffuse. It’s also true that Jupiter sort of “shepherds” the asteroid belt, so unlike something like planetary rings, it’s a much more complex system. I hope that goes some way to answering your question, which wasn’t dumb at all.