"You are not insinuating no sights at all, right?"
This isn't a rifle story, but a related handgun story.
When I took Gunsite's basic handgun class, we were four days into the class when we had the night shoot. We did some flashlight work and then the instructors had us do something bizarre. We did a drill where we drew our handguns into a good solid Weaver stance. The same stance we had been shooting out of all day for the last four days. We were then instructed to fire a five shot group on the target in the pitch dark (we might have shut our eyes, I don't remember). When everyone was done, the rangemaster said, "Before anyone turns on their light, I am going to tell you that these groups will be the best group you shot all week". And, of course, he was right. The groups were right in the COM and were basically one ragged hole. The alignment was achieved completely from our stance and body index.
Back to rifles.
Let me first say that I am certainly no expert on anything. I am only repeating what I have been told in various classes. I have never been in combat or worked in law enforcement. This all may be BS, but when I was told this stuff, I tried it and it works for me and it makes sense. Ok, when most people shoot a rifle, then stand almost 90 degrees to the target in an extremly sharply bladed stance. This is the classic off-hand position. This is not how I was taught to shoot these types of rifles. The stance is basically facing the target stright on, with about a 30 degree blade. Picture youself walking straight toward the target with the toe of the weapon in the pocket and pointed down at the ground at about a 45 degree angle to the target. When you engage the target, you simply pivot the weapon up on it's hinge until the sights are in front of your eyes and fire. Your eyes remain looking at the target and your head doesn't move at all. If you play around with this pocket and your orientation to the target, you will see that it is easier to keep the toe of the stock in the pocket when you are standing more square to the target than if you are bladed off at almost 90 degrees. When you are bladed way off, this is why you will need to "chicken wing" or raise your arm way up to make the pocket. Another example would be to imagine you were in a fist fight with your opponent. You arn't facing 90 degrees away from him. You are in a good steady stance. If he hits you, you arn't going to lose your balance and fall down. You stance is solid to absorb that recoil. Contrast that to the severely bladed stance where the butt of the rifle is almost ready to slide across your shoulder into space.
When stationary you are squared to the target in this fighting stance. You arn't standing bolt upright. Your knees are not locked. You are bent forward slightly at the waist. Just like you are ready to box. Note that with a 30 degree blade the sights now come right up to your eye.
Leave that arm out there and someone will shoot it off.