No it doesn't. It has to do with reference frames. In general relativity, all reference frames are equally appropriate -- the Lorentz symmetry enjoyed by inertial observers is no longer a preferred symmetry. What cosmik is saying, however, is that some spacetimes possesses sufficient symmetry to define a global time variable (just like one does for inertial frames in special relativity). In these spacetimes, this time variable is a 'natural' choice to run a clock by. In our FRW universe, observers comoving with the expansion (at reast wrt the CMB) are in one such frame. We are (very closely) comoving observers, and so this is the clock used by modern cosmologists. But this time is still no better than any other -- one can choose whichever frame one wishes; some are simply more convenient than others. (To see what I mean by convenience, imagine using galaxy-centric coordinates to plan satellite trajectories around the Earth -- obviously one should use geocentric coordinates for such a feat.)
