Tom,
This is just a guess, but I strongly suspect that the closer you have the scope to your balance point, the less it will affect the bullets point of impact. I am currently working on an over and under rifle for a client who wanted a scope incorporated in his new gun. I am regulating it with the scope first. I will then set the iron sights to match that point of impact. It seems to be the rule that if you are going to have a scope mounted on the gun, that you need to regulate it with the scope present.
As soon as I have done both I can tell you more about the affect it has on the points of impact by removing or adding the scope. I am also fairly certain that because of the rotation in a side by side, this effect will be worse on them that the over and under. Also his scope is a lightweight red dot which probably won't affect the gun as much as a heavier scope would.
You also bought up a good point about factory scope mounts on rifles. If you will notice, they all set them as far back on the barrels as possible, probably so the scope will be as near to the balance point as possible.
Bob H.
