Originally Posted by tyrion

I don't think that's entirely true. A bike will turn in the direction that it's leaning, even if the wheels are perfectly straight, because the circumference of the tire on the leaning side is smaller than the circumference of the center of the tire. When leaned over the contact patches become conical.

This is much more apparent at motorcycle speeds and fat tires, but the physics still apply to bicycles' slower speeds and skinnier tires.