One thing not often talked about is how long the bullet or arrow is in flight. Every micro-second that bullet takes to get there the odds of that animal moving increase. So yeah, some people can shoot 1,000 yards at paper, but paper doesn't all of a sudden decide that forb looks mighty tasty, I think I will take a step and eat it---and boom there is a hit in the paunch or hind quarter.
The other thing is that guys that shoot long distance at the range don't have to contend with is uneven winds, thermals, etc that might be different a half dozen places along the path of the bullet. How many times have you read about a hunter that all of sudden felt a draft on the back of his neck that resulted in the animal smelling the hunter and bolting? What are the odds then, that a draft like that could happen somewhere along the long path of the bullet?