The bears will generally leave you alone as long as they’re catching enough salmon on their own.
I’ve fished Alaskan rivers, but yeah, that wouldn’t be my preferred spot.
A friend of mine went on a guided fishing trip to Alaska. On the morning of the first day he noticed the guide wearing a 44 magnum revolver and asked if he could look at it. Upon inspection he noticed there was no front sight. He asked the guide why there was no sight.
The guide replied, “Well, if I have to shoot a bear, after emptying the cylinder into him it won’t hurt so much when he shoves it up my ass.”
I would disagree. Grizzly bears generally are inland while brown bears are either coastal or along major water ways. They are the same species, but are different subspecies, with considerable dietary and behavioral differences. Grizzlies tend to be a bit more aggressive than brown bears. The ones at Brooks Falls are all brown bears.
That link may not work, but here is the relevant section from the National Park Service:
2. What is the difference between brown bears and grizzly bears?
All grizzly bears are brown bears, but not all brown bears are grizzly bears. The bears you are watching on the cams are brown bears. Grizzly bears and brown bears are the same species ( Ursus arctos ), but grizzly bears are currently considered to be a separate subspecies ( U. a. horribilis ). Due to a few morphological differences, Kodiak bears are also considered to be a distinct subspecies of brown bear ( U. a. middendorfii ), but are very similar to Katmai’s brown bears in diet and habits.
Even though grizzlies are considered to be a subspecies of brown bear, the difference between a grizzly bear and a brown bear is fairly arbitrary. In North America, brown bears are generally considered to be those of the species that have access to coastal food resources like salmon. Grizzly bears live further inland and typically do not have access to marine-derived food resources.
Besides habitat and diet, there are physical and (arguably) temperamental differences between brown and grizzly bears. Large male brown bears in Katmai can routinely weigh over 1000 pounds (454 kg) in the fall. In contrast, grizzly bears in Yellowstone National Park weigh far less on average. There have been no documented cases of grizzly bears weighing over 900 pounds (408 kg) in Yellowstone. Additionally, grizzly bears seem to react to humans at greater distances than brown bears.