Don't think it is the shell in that case. The guys that hand load are the guys that spend more time getting to know the gun. I was surprised at the folks that stop by that have NO CLUE the POA/POI of the gun they had. The guy that gets into the numbers game I don't think have a better choke, gun or shell. I think they have learned the gun. 50% is equipment and 50% is hunter
No question that guys who load their own spend more time at the range and therefore are surely going to do a better job performing well when they pull the trigger, compared to the average Joe who is looking to buy the cheapest stuff he can find and then starts shooting at turkeys.
I am not sure exactly what your definition of the "guy who gets into the numebers game" is, but I can say with confidence that the ammo makes a huge difference in performance when it comes to whether a turkey lives, is crippled, or dies when the guy pulls the trigger. It gives the biggest bang for one's turkey hunting buck. I can only speak for myself, but I can't see the point of spending thousands of dollars to hunt every year, and then skimping when it comes to the moment of truth, just to save a few dimes.
IMO, whatever one shoots, just make sure you know what the pattern of shot is doing out there, and then keep within the shell's limitations. As ethical hunters, it should be our goal to have a dead turkey, every time we point the gun at one and pull the trigger. And since most hunters don't play the numbers game enough to know better, I'm afraid a lot of hunters are going to fall for the deceptive 60+ yard marketing job Winchester is doing.