In the Injured Arm question, the person in the question has just broken his (or her) arm. He is in pain, to some extent in shock, bewildered and completely unprepared to attempt a rappel with only one arm. And the other arm has to be protected against further damage, adding to the awkwardness and tension.
In the One Arm question, the injury occurred six months ago. The woman is no longer in pain, and has had nearly six months to develop techniques to do things with only one arm, and has had time to substantially strengthen her remaining arm. I am not a climber, so I don't know how far "developing technques" would extend to rappelling with one very strong arm, but that's the question, isn't it?
A permanent or semi-permanent disability is different from a recent injury.
One is a question about handling an emergency in TGO safely; the other is a question about how much a prepared disabled person can do in TGO. We do disabled people a disservice by equating them to emergencies in TGO.