That is an interesting situation. If I was the team I would compromise by setting up a rope system and attaching the willing hero guy to the end, wearing two pairs of carhartts and a flak jacket, give him an frs radio, lower him (so he has both hands free, way safer than rapping), let him bag the dog, then raise him with a mech adv. system. Only the guy who wants to risk it is exposed to the danger, and the op is done in a much safer style than what looks a little out of control outlined above. Of course some serious release forms would be tossed around if the sheriff is involved. Maybe that would work out. Rapping down to a crazed 80lb animal is hanging it out there a bit for sure.
What if it were an injured horse down there? Is it still a go?