I've wondered that same thing, especially for early season bear hunting that's more of a hike than a real "hunt."  I have a lab (the bird dog) and a Australian Shepard/Blue Heeler mix (the useless but kind of cute dog) and I would hope that no one would believe that I would try to run a bear with them.  On the other hand, I was worried about it, so I've never actually taken them with me when I've had a rifle.  God forbid I should wound one and my dog actually catches up with it while it's still alive for some reason.  I'd anticipate a dead dog.