The physics of it...
Your opening post is fundamentally correct
Ray B.
In simple terms the moment the powder charge is ignited two actions start
simultaneously: in one direction the bullet starts traveling through the barrel, and in the opposite direction the rifle starts recoiling. This is just physics.
Of course the bullet takes a very small time to travel down the barrel, but during this time the rifle
does move, and how the rifle moves and where the barrel points as the bullet leaves the barrel determines where the bullet will hit. Again, simple physics.
Recoil per se has no intrinsic effect on accuracy, but recoil control, and recoil control consistency are critical to accuracy.
This is the reason why shooters looking for ultimate accuracy (from 50 meters .22 LR 3 Positions Olympic Match, or prone English Match shooters, to 1,000 yards Palma Match shooters, to military or law enforcement snipers, etc.) will never shoot a rifle that they have no sighted
themselves, because the variables in human nature, shooting form and recoil control techniques are such that
no two shooters control recoil the same way.
This is the reason why British double rifles makers in the golden age asked their clients to come and shoot the rifle during the regulation process, because they realized that a critical variable in the double regulation is the control of the recoil and the yaw. The same .470 double rifle will assuredly shoots to different points of impact, and likely produce different group sizes, with 120 lbs Jack who rolls with the recoil and 230 lbs John who fights the recoil.
Of course, the effects are magnified with high-recoil rifles, but the principles also apply all the way down to .22 LR rifles. I shot pre-Olympic for about 5 years with an Anschutz 1913 Super Match 54 rifle that weighed 11+ lbs, and it is hard to believe that shooting something like that, prone, with competition sling, compression jacket, etc. still comes down to consistency in recoil control. With an 11+ lbs .22 LR rifle shooting low speed match ammo, for crying out loud, one would think that there is no recoil to control, right? Wrong...
Now get to .458 Lott or darn anything in between, and you get the implication:
the biggest factor in shooting accuracy is recoil control and consistency in recoil control. The faster and bigger the recoil, the more difficult...
Beside the obvious: the caliber and load (specifically: bullet weight, powder weight, burn rate, and barrel timing, i.e. the time the bullet takes to exit the barrel), the factors at play include virtually anything you can think of: rifle weight, stock design, stock fit, recoil pad characteristics, shooter position, rifle support, shooter mass, shooting form, shooter clothes, etc. For example, a rifle will change point of impact (POI) subtly (or no so subtly) if you as much as change the recoil pad on it... It may not show much difference between a 3/4" and a 1" Decelerator, but experiment adding a slip-on absorbing recoil pad on a military rifle that has a steel butt plate and you will be surprised at the outcome...
So, the reality is that shooting with or without a lead sled
does produce a shift of POI, not by feet mind you, but by an inch or two typically, because the recoil control dynamics change, even if we do not typically see it when shooting at game where, truth be told, we do not measure POI vs. point of aim as long as the bullet lands somewhere within a few inches of where it was intended and kills cleanly, but if you want to verify the lead sled effect, there is nothing simpler. Shoot 5 rounds with the sled, then 5 rounds without the sled, you will see a shift of POI, it may be big or small, depending on your technique, but it will be there, it is simply the physics of the application of forces.
I will be the first to say that as long as the shift of POI does not exceed 1" or 2", who cares !!! Heck the wobbling of the rifle on the sticks or in field shooting positions, sitting, kneeling, or, God forbid!, standing off hand, will create a lot more variation in the POI that the use or not of the sled, but you will never see a sniper or competitor use a sled to sight their rifle...
In the end, this is why some calibers (especially those that recoil fast and furious) have gained the reputation of being "difficult to shoot well." Of course there is nothing difficult in aiming them or pulling their trigger, and nothing inherently wrong with their ballistics, but keeping them pointed in the right direction under fierce recoil is difficult, especially when the recoil is fast - hence when the bullet still has a substantial portion of barrel to go through while the rifle moves a lot, and doing it consistently always the same way is even more difficult...
Changing the characteristics of the rifle (adding or removing muzzle brakes or suppressors, etc.) obviously change the dynamics of the recoil, hence the POI.
Then we can add the next layer to the discussion, which includes all the types of shooter errors (general category: flinch) caused by recoil that either scares or hurts, or both...
Some appear to be impervious to recoil but most of us are not, and this is why most of us, myself certainly included, shoot a .223 a lot better than a .458