He may be like me. I shoot handguns with left hand and right eye or right hand left eye or right and right or left and left. Why? You never know what you may need to be good at in a fire fight. I do the same thing with my long guns except when there is a scope. With a scope I keep the right with the right and the left with the left for mechanical reasons. But I have shot right/left and left/right with a scope. It is not comfortable but I do it well. If you don’t practice like this, try it next time at the range. you’ll be surprized how quickly you get good at it.
I’ve seen plenty of people struggle with “different-eye” dominance, if that’s what it can be called.
The son of a friend of mine probably was a natural lefty when he was little. But as he grew up he learned to write, throw, etc. etc. with his right hand.
His dad wasn’t a hunter or shooter so I have taken them both out on occasion just to plink. The first time the young man raised the rifle, he was holding it righty but cramming his head down on the stock to get his left eye to the scope.
I told him to go ahead and hold the rifle (.22 mag) left-handed. He insisted on going righty but at times when I would glance over he would be cramming his face down there again without even realizing it.