Take a buddy to the range with you. Preferably a wide outdoor range not in use by anyone else. You stand facing away from the target area. Send your buddy down range to set up a target in a random position. When he is back up range have him yell go or something like that. Fall to the ground landing on the opposite side of your firearm. As you are falling, grab your firearm and attempt to locate your target. Position your sites onto your target as you are rolling onto your BACK or other stable firing position. Being on your back gives you ability to to aim 360 degrees around you incase someone comes at you from another direction. Lay on your stomach and someone comes at you from behind, you have to take the time to reposition your body in order to get a shot off directly behind you (or atleast a well aimed shot.)
Thanks. I was afraid I was going to have to ask the question again. I remember practicing the position you describe in police firearms training, but the (very good, IMO) instructors explained that particular rationale, I missed it. It does make sense as you describe it.