It isn't true at all. Assuming that the expansion is isotropic, then space between the pair of points expands at a rate proportional to the current separation of the pairs of points. The distance from us to the pair of points is not relevant.
And actually it is, observationally, but opposite to what has been suggested. Distant pairs of objects will be observed to expand away from each other more slowly than similarly separated pairs that are closer, as the more distant pair are being more red-shifted.