Actually, rats are pretty smart...you can train them to do all sorts of tricks, and the buggers will actually answer to their names...so a particularly smart rat could probably grasp some of the basics of ninjitsu, anyway...
Plus, if the mutagen made Splinter smarter, perhaps it would've given him access to memories (and teachings) that he couldn't have fully grasped before, yet were still buried deep in his mind.
One possible explanation, though we clearly see the rat doing hardcore martial arts in the film and games.
I don't remember having seen the comic origin pages.
In the cartoon, I'm thinking Splinter should've become a humanoid rat-turtle, since he was in contact with the rats and then the Turtles.
