You are bringing back memories. I had competed in small rifle as a youth. I also had my share of rifleman stories, like nailing squirrel at 100 yards in the head with a .22 Hornet, killing a starling at 75 yards with an air rifle, breaking a lightbulb at the same distance at night (light was on!) and shooting through Lifesaver candy at 30 yards.
Needless to say, I had the art down pat with IRON sights. OK, the squirrel were through a 4 power scope.
In my US Army Basic Combat Training, there was a plethora of non-shooters. I spent many times explaining the mechanics of the rifle to these recruits but none as much as PVT Jeffery Creek of IL. Creek could not shoot. Period. The Drills had to zero his rifle for him and he still had a major problem keeping 3 rounds on the 25 meter zero target. I was used to keeping 5 shots in 1/4" at 2/3's that range and knew there was a shooter problem there.
I carefully watched and immediately recognized the problem. Creek was cross-dominant. He was trying to use his left eye with a right handed hold. After one string, I told him to shoot left handed and use his stronger left eye. To be absolutely sure, I did the field test. He was cross dominant!
Sure enough, next string Creek ate the center mass. Next string the Drills saw him shooting southpaw and asked him why. Finger pointed to me and I was aksed if I thought I knew how to shoot better than the cadre. The answer was no mystery to me but I kept quiet as I rather have those ignorant drills think they were right. I regret not taking it further but decided 8 weeks was long enough and didn't want to be recycled for showing off.
Drill forces Creek to shoot right handed with his right eye. Sure enough, groups vanish. They then send him to the TMC to have his eyes checked. The profile he got was simple. Shoot left handed. Vindication was mine!
Yes, cross dominance IS a major problem in shooting.