My reaction to this is that even if you are packing, a deranged psychopath who is bent on killing someone is not really going to give you a chance to a fair shootout, now is he? I would imagine said psychopath sniping you from behind some hiding place, or killing you in your sleep, so the gun wouldn't really help.
Word. Which then suggests something about the person who is adamant about bringing guns on the trail for "protection"; given the above analysis, the gun carrying hiker out for a walk, in order to adjust the odds in his favor, would need to regard every hiker they meet with immediate, high level suspicion and fear and keep a close eye on their every move as they pass one another, not to mention a finger on the trigger. Now if I'm that other hiker, I'm pretty sure that this suspicious, gun packing man giving me the stinkeye as I go by is going to leave me a lot more scared of him than the other way around.