One does not know what to make of this story.
If true, it means that there was no rooftop sniper, and indeed, the shot must have been fired from near, because it is hard to judge the direction of gunfire. The story by the doctor could support the allegation that she was shot by a member of the crowd - who had apparently also fired on a number of Basijs. If the man whom they apprehended had been a member of the Iranian security forces, would not they have released his picture?
But I don't know whether the doctor's testimony is genuine.
Apparently? There have been hundreds of videos and photos show Basijs with & firing guns. I haven't seen any videos or photos of any protester with or firing a gun? If you have, I'd be interested in seeing it.
CORRECTION: show = showing