Didn't see the video you refer to, but I suspect they shot the bear while it was swimming and helpless
They were on land, were behind the bear and shot it in the rear, it bled out in its den and they dragged it out and skinned it. Was a home made film my Pastor showed us of the time he was in Alaska doing Salvation Army stuff. He was there for many years with these hunters.
Does this clear it up? They used their heads and know how to kill it safely as they do everything they kill like whales from canoes etc.
First defense is your smarts, dont have any? well you wont be able to defend anything with out them, smarts that is.