But Naruto doesn't use Kyuubi's chakra to do the Rasengan does he? He's never had to access it I don't think, he uses a clone to help him but I think it's just about controlling your chakra in a certain way, not the amount of chakra you have.

Kakashi wouldn't ever use Rasengan anyway, it's not his style. The Rasengan is big, loud and clumsy, where as the Chidori is sleek, quick, and cool, much more suited to Kakashi's style of techniques.