Comet collisions...
Comets colliding with other comets during our young solar system's time may have been possible. Yes, I know, it may have been rarer, if that, during the more recent time when Saturn's rings occured, but there could have been the possibility of a cometary collision with an asteroid. I'm just bringing up possibilities since I wasn't there. The most probable cause for the rings could have been an asteroid to asteroid collision as you put it, or rock to rock. Still, there's seems to be a lot of ice rocks in those rings.
Marcia