I actually shoot groups from unfouled barrels quite often and with most of my rifles I don't see much difference but you need to actually get a barrel clean of power and copper fouling completely for this to work. If you don't get your barrel truly clean then you definitely need fouling shots. I'm talking about either quality custom barrels or very good factory barrels here and yes I own a few remarkable factory barrels.
Give this theory a try. Now if I were competing (which I don't intend to do) I'd pad my bets and foul any barrel before actually shooting for group but for hunting I've proven over and over through my 50 years of shooting that I can still get great accuracy even from my first shot from a truly clean barrel.
I hope y'all are removing most of the oil from your barrels before that first shot after cleaning. If you're not then there is your need for a fouling shot proven. Not only is it critical to remove most of the oil from a barrel to reduce harm to a barrel from that bullet having to deal with little globs of oil intermittently scattered down the bore but custom barrel makers will tell you that shooting an oily bore with cause small pits in the barrel from the hydraulic action of the bullet compressing that oil as it speeds down the bore. Plus that oil will cause erratic groups.
The proper technique is to get the bore squeaky clean and then to dry patch out all your solvents and oils and then to apply some fine oil such as Kroil with a wet patch followed by a dry patch to get most of that oil out leaving a very fine film. Then you're good to shoot.
Here's another thought. I never put a gun away with a dirty bore. Under that powder and copper fouling you will end up with trapped moisture and then rust. All rifle barrels rust. How much they rust is up to you but if you clean a bore and then put in a quality oil your chances of rust are GREATLY reduced. You can run that dry patch I suggested earlier just before hunting or shooting at the range. See? I just told you how to go hunting without having to fire a fouling shot or shots.
If you're hunting game and your shots are likely to be 300yds or closer then the dry patch to remove the bulk of the oil is enough. If you're likely to shoot beyond 300yds then you should know your rifle well enough to know how many fouling shots (if any) you need to get it shooting to it's peak accuracy.
When you get home or back to camp and you haven't fired your rifle then remember to run at least one oily patch down your bore to prevent rust and remove any grit that might have found it's way in your bore from a day of carrying and then a dry patch again before hunting. If you have fired it either one or just a few shots I'd suggest getting it clean again.
At some point in almost any night in almost any climate you will hit a dew point where the air will become very moist and that is death on non oiled barrels and if you're out hunting it won't take long for rust damage to start in that barrel. If you spend much time with a bore scope you'll learn to spot rust and rust damage. It's a crying shame to let a good barrel suffer from any more rust damage than the tiny bit that will inevitably happen if you are diligent about keeping at least some oil in the bore when you're not carrying the rifle ready to shoot.
Just one man's opinion backed up by many years of learning the hard way and ruining several barrels before I figured out the above stuff....
