There is another point to be made about insisting on the reentry - Columbia didn’t have propellant to reach the ISS, and life support couldn’t be extended until a rescue mission could be mounted. A rescue mission would be further complicated because the docking hardware was not needed for this mission and was removed, and there was no airlock for EVAs (and no EVA suit on board), again, because it wasn’t part of the mission.

If a rescue mission could have been mounted, it’d be something straight out of science fiction - tying ships together with cables and shuttling astronauts in their orange pressure suits through the side doors of two disconnected shuttles.