I first heard the saying I think sometime around the loss of Colombia. Maybe before, maybe after. By the return to flight, it was most certainly more true than false. By that time the shuttles performed very few non-ISS flights. I think that Atlantis flew a service mission to Hubble, other than that I can't think of any other shuttle flights that didn't go to the space station.

Columbia was heavier than the other orbiters, so she was flying the non-ISS missions from about '98 until her demise. After that US satellites were launched on disposable, unmanned rockets like the Deltas and Atlas.