I've lived in SW Alaska for several years and I've fished in SW Alaska for I don't know how many years. I have encountered hundreds - yes, hundreds - of brown bears during that time. Some were quite close. Had a fishing guide tell me once, "Watch your back cast. There's a bear back there." I saw a bear come out of the grass by the bushes behind my son once. We were fishing opposite sides of a small feeder stream. The bear was probably 3 yards away from my son. I was floating down a river with a friend. We were in a self-bailing cata-raft. The river came around a corner and the current pushed us to a far bank. Suddenly we were within feet of a sow with 2 older cubs. My friend, closer to the bank than I, could have touched one with his fly rod. I've chased bears out of my yard and away from my truck at the dump. I would say that I have a fair amount of experience with brown bears and I would make the following observations:
1. I don't trust bear spray. To be effective, you need to get it into the bear's eyes, which means you need to practice and the canisters aren't cheap. Further, their range is not long and a strong wind can make you miss. There's also a better than even chance you'll get it on you. For that reason, I prefer a pistol. For my own tastes, I use a 10mm with 200gr buffalo bore bullets. I just picked up a FN 510, in part because it has a 22 rd magazine. I know other firearms (.44mag and larger) have better penetration but: they're heavy; the gun and the ammo is expensive; recoil is substantial, which means re-acquiring the target is harder; and they carry fewer rounds. I don't claim the 10mm is perfect but it does a lot of things well. I'd rather have 15+ shots with B+/A- penetration than 6 with A/A+ penetration, especially when I can get off 5-6 shots in 3 seconds instead of 2-3 shots.
2. Bears on salmon streams have a different attitude than bears elsewhere primarily because there is so much food. While I give bears a lot of latitude, the catarafts I use to float down streams will frequently make bears scramble away from the banks if the bear feels the raft is too close. Keep in mind there are documented instances of bears attacking cars, boats, and even trains. Not saying the bears always live but they will attack large objects if they feel threatened. My own theory, which comports with numerous other people's experience, is that the sheer number of salmon in these streams make the bears far less 'possessive' than they would be over, say, a moose kill. That isn't to say that the bears are harmless or that I am careless. Rather, a bear encounter by a salmon stream is a lot more likely to involve the bear fleeing than a bear encounter on a narrow path where the bear feels hemmed in or coming across a bear over its kill. Small cubs near a sow can dramatically change this calculus.
3. The key to such a bear encounter is to remain calm as these guys did. This video is rather short and appears to have started shortly after the bear came out of the woods unexpectedly. The very LAST thing to do is to run away. That triggers the bear's predatory instinct. Rather, they stayed still and calm and did nothing to aggravate or antagonize the bear. That was 100% the right thing to do.
4. If it had been me, I would have done 2 things differently. First I would have assumed my "bear stance" and talked to the bear. By bear stance, I mean I would purposefully make myself look bigger. I stand with my legs spread farther apart and put my hands straight up. DO NOT LOOK THE BEAR IN THE EYE. Instead, slowly back up while talking in a soft, mellow sing-song voice. My own chant is something like, "Hello, Mr. Bear. I am leaving. You are fine. Blah, blah, blah." The words obviously do not matter but a low, calm voice demonstrates you are not a threat. Slowing backing up shows you are not a threat and gives the bear lots of room. Given the proximity of that bear, I would likely have my pistol in my hand (use a chest holster like the Kenai chest holster from gun fighters, inc.) even if it's in the air. That way it's ready in case that bear gets aggressive.
5. The second thing I would have done differently is I would have waited until the bear had passed beyond me and was facing AWAY from me and I would fire a warning shot into the river. I know some on here debate the efficacy of warning shots but I personally have used warning shots to scare away 3 bears over the last 20+ years. This is one reason I like a 10mm - 1 warning shot is a small price to pay for potentially scaring a bear away because I would still have 15 rounds or so if the shot did not work. I would have made the shot when the bear was facing away because the bear will run away from the shot. If the bear is facing me and I fire a warning shot, that bear could come right at me.
6. I would not have recorded it but that's because I've got plenty of bear videos and with one that close, I would rather have a pistol in my hand with one that close. I have a bear video I'd like to attach but I can't for some reason. I have it in .mov and .mp4 formats and it's only 3MB.
7. Legally speaking, at least in Alaska, there is no legal justification for shooting this bear. Many people in rural Alaska will have had similar experiences and would not be kindly disposed to shooting a bear that wandered through a camp like that. Damaging property or showing aggression would be different but if one of those guys had shot that bear and that video was played at the trial, I am not real sure an Alaska jury would be very sympathetic. I say that because a friend tried a case involving a pilot who shot a bear in defense of life and property (DLP) while moose hunting. The guy's testimony was about how the bear was aggressive and he was really scared but when they introduced the hide into evidence, it was clear the bear was a younger bear and not large. The jury convicted him of unlawfully taking a bear. You should keep this in mind if you are ever fishing in Alaska and you encounter a bear. Hopefully you'll have a guide who will be armed and can provide a good perspective because they deal with bears about every day. But its something you should keep in mind if you are in that situation.
I know it's a long post but I try to post only when I have something constructive to add. There's a lot to deal with in these scenarios. I don't know where these guys are from or their own experience. With all that I've said, I think they did pretty well by playing it cool and keeping calm when a large bear just comes out of the woods like that. While I would do a couple of things differently, I think over all, they did just fine. They did not provoke the bear, nor did they cause the encounter, at least from what I can see in this video. I appear to be in the minority, but if you're fishing and a bear comes out of the woods, what do you do? They did the most important thing: they did not agitate the bear or get it riled up.