I think the title of the thread is accurate, but this is followed by arguments about it that seem to be based on misconceptions. Anyway, gravity does "slow down" time, or more accurately it affects the time rate of change of everything. But the effect has to be measured by bringing clocks together, and this means moving them (you don't say?). Once you introduce motion you introduce another physical effect; you "break" the symmetry (of the 'global' effect of the field on local frames), by how much depends on how you move the clocks together (i.e. to the same rest frame). If you bring two clocks to the same rest frame, then obviously they no longer disagree about position. That would extend to positions of other apparently fixed objects, such as the sun (if the clocks are on the earth).