Cheney didn't mis-identify his game. He wasn't shooting AT the man, he was shooting at some quail that were flushed from the covey. Sounds like at the instant Cheney pulled the trigger, the man stepped into the path of the birdshot.
With the sun behind him, from what Mrs. Armstrong said.
Don't have a dog in this hunt,but I'll explain what happens when bird hunting for those who don't hunt.A hunter is taught from day one that when the bird is in flight,start with the bead of the barrel behind the bird.As you catch up with the bird,you pull the trigger as the bead proceeds in front of the bird.This is called "giving a lead".You never stop the barrel,aiming,like you would with a rifle.The shotgun barrel is moving in a sweeping motion(arc) and you always follow through,past the bird.This gives you a wider shot dispersment,much like taking a water hose and swinging it from right to left.
The reasons for this is,the bird is a moving object.A tiny,fast flying, moving object.If you stopped the barrel as the bead was on the bird,you'd shoot behind him every time.With that said,depending on how far the bird was from the VP,he could well have been sweeping the gun 140-160 degrees before he made his shot.While looking down a barrel,which produces tunnel vision,it's easy to focus on the object and not behind it.(No excuse,but hopefully a little light on the subject.)