I'm shooting Federal #4's. It has that Flight Control wad thingy. In the first 10 yards, that thing is a bullet. Most of my shots end up with the wad hitting the bird. So you're not talking about deflecting part of a shot string, you're deflecting the whole load. I'm also sighting through a scope; the parallax induced by the scope and its mount means I have to be conservative in judging what will and won't deflect a shot. Bottom line: I'm careful.
There are a bunch of old-schoolers that can't stand the idea of a scope. I simply don't have the eyes to do precision shooting with beads or irons anymore. Scopes can be a problem close in, and they offer challenges of their own. One of the big problems is parallax. The crosshairs are quite a ways off the center of the barrel. As a result, where I'm looking isn't quite the path the shot is going to take. Where I'm looking is a straight line. Where the shot is going starts lower and works itself gradually up towards the line of sight. The other problem with a scope is that objects close in will appear dramatically out of focus. As a result a little transluscent blob in the lower half of the scope may be just a leaf, or it may be a huge branch. If I'm in brush, one trick I try to do is to close the eye that's on the scope and give one last look through the other eye to scope out obstructions before actually commiting to the shot.
The vast majority of my setups reflect that. I'm usually in a treeline, shooting out into a pasture or clearing. I rely on the tall grass at the edge and the shadows behind to hide me.
I have a guess, and it's only a guess. I'll throw it out for discussion. My guess is that there is enough of a pressure wave in front of the shot string that things like grass are going to lay down at close range. Anything that won't lay down will probably screw up the shot. As you get further out, the situation reverses. The benefit of a shotgun's spread works in your favor-- a twig will deflect individual shot, but not a large percentage of the total. On the other hand, if the shot string encounters grass at the longer end of its range. The grass will now do a better job of screening the gobbler.