WMG / Mega Man II

The Sakugarne is really the future incarnation of Rush

Since the future Mega Man was turned into Quint, it stands to reason that Rush exists in some incarnation in the future too, and that if the Blue Bomber himself could be captured, so could Rush. More to the point, if you look at the Sakugarne it has the same red, white and gold color scheme that Rush does, it teleports into battle the same way as Rush (and Mega Man and Quint), and Quint rides it in a similar way to how Mega Man uses several of the Rush Adapters. It therefore seems likely that in addition to making the future Mega Man into an evil robot, Wily decided to make the situation as humiliating as possible by transmogrifying his beloved pet into a bizarre and useless weapon that Quint would be forced to use every time he want into battle.