If I knew I was going to run into a dangerous brown bear, I would carry nothing less than rifle in .375 H&H. I might take one of those Marlin Guide Guns in 45-70 if I had tested it enough to know it was reliable.
My son in Alaska always carries a 45-70 with hot loads with him when fishing in western Alaska...just in case! When hunting brown bears, the minimum is a .338 mag...
JC
Many years ago I read a story written by a native of Alaska about hunting for moose, sheep, goats etc in grizzly country. Most of the locals at that time carried 30-06's when hunting. I don't recall the distance, but the writer said that when a grizzly got to that point the shooting started.
Since the study that started this thread talks about people who hesitated, it would be interesting to read that story again.