One of the best examples of the stress and rush related to a charging dangerous animal is the film below.
This movie involves an African lion instead of a Grizzly or Brown but I believe the message is the same.
To give some background to the film -- the professional hunters are attempting to kill a small male lion who had actually killed a man a few days earlier.
This film may give some perspective to the limited amount of time the hunters have to get their shots off and the speed of which the lion was on them. Grizzlies are actually faster than African Lions.... Notice the missed shots kicking up dust in the background.... These are seasoned professional hunters who, under the stress of the charge, missed several shots and almost died because of it.
Then consider the dense habitat most North American big bears live in, their speed, and the danger from an angry adrenaline pumped bear will be better understood.
http://www.youtube.com/watch?v=0CNgwZgoKFc
TC