Rifleman, you're probably overestimating my expertise, but I'll do my best.
The bear that killed Treadwell and Huguenard was indeed an old, hungry one, as you mentioned. It was also, very likely, well used to the presence of humans at very close range, as Treadwell had been camping in that area for a long time, and refused to take even the most basic precautions, such as carrying bear spray, or having an electric fence around his tent, which is standard practice for bear researchers, even some hunters -- anyone who deliberately camps in an area where they know there are bears.
If you happen to run into such a bear while hiking, you won't know what shape it's in. The stats do show that for those encounters, bear spray is your best defense. If a bear approaches your campsite, again, the odds are that the spray will stop an attack. If the bear comes back, that's when you may be very glad you have the shotgun...
I know some people who had to shoot a polar bear under such circumstances while on a canoe trip in the Arctic. They tried to avoid the bear as best they could -- moved their camp several miles downstream to get away from it -- but it was clearly stalking them. Finally, it approached their camp in way that said "You are prey" -- at which point they shot and wounded it, and it left. They called the Canadian authorities, who came in by helicopter and tracked and killed the bear. I've seen the video they shot of their encounters with that bear, and there's no question that it was hunting them.
So, yes, it was very good that they had a shotgun along. But note that even with plenty of time to get the gun, and plenty of time to aim, the shooter wounded the bear rather than killing it. Scary. And that's one of the big problems with firearms: you can miss, or wound, and then you may have a hurt, enraged bear charging you -- this is the reason more people are injured defending themselves with firearms than with pepper spray. It's harder to miss with the spray (although the bear does have to be rather close), and it does in fact stop the bear. With a firearm, you have to make a brain shot to be sure of stopping a charging bear, and that's a very small target that's bouncing around while you're trying to hit it.
Originally Posted by Nasty
Unless armed and on a hunt, why does anyone fail to pay attention to where the bears are and then, often intentionally, get within 1/4 mile of them?
Avoid the bears people...they were there first.
Well, you can pay all the attention you like, and there may still be a bear where you can't see it, in thick brush or around a corner of the trail. I've camped a lot (on long canoe trips) in brown bear country, and we always scout a potential campsite for bear sign. If we find any recent tracks or poop, we just move on.
But as for intentionally approaching a bear just for the heck of it -- that's dumb. Most bears who aren't acclimated to humans will head the other way right quick, once they scent or spot you, but why push your luck?
There's a surprising number of people, though, who think it's Disneyland out there, and all the critters are cute and friendly.