RadioAstronomer will correct me if I'm wrong, but if you think of it like a balloon, it makes sense. C would be the max speed you could travel over the surface of the balloon, but it does not have anything to do with the rate of expansion of the balloon, which is what actually causes the galaxies on its surface to move apart.
You've got it.
The reason for this is that the speed of light limit applies to the movement of matter and transmittal of information; it does NOT apply to spacetime itself (as spacetime, the "fabric" of the Universe, has no mass and isn't "information.")