RE: Snuck up behind a Cougar!
To me having a pistol or knife at my side isn't so much to fend off the animal but to grab for in desparation after the animal is attacking me. I'm no expert but in my mind if I'm on the ground being attacked hopefully I'll have the presence of mind to grab for the weapon to get the critter off me.
Who knows? The reality of it is pretty bleak but I'd rather have that option than not.