One of the problems is that most people, even many Alaskans, have never seen an adult brownie up close.
When someone describes some guy in the interior taking a "brown bear" with a .223, he's talking about a mountain grizzly that might go 350 or 400 pounds, tops - yeah, that's technically a "brown bear", but... it's on a whole different scale. There are black bears in the eastern US which grow larger than mountain grizzlies, sometimes much larger.
That grizzly seen in Denali, while an impressive animal, is only 1/3rd the size of a coastal brown bear. And those brownies seen along the rivers on the Kenai are almost never adults.
People just don't know!
I assure you that nobody down here in coastal brown bear country (even them "crazy natives") hunts brownies with .223's and .30/30's. I know it's been done, and I know it will be done again. And people will take them with .44 mags, bows and arrows and muzzle loaders - but it's a stunt! There's a friend or a guide standing by with a .375 or .338.
You can certainly get away with taking big animals with light rifles. And probably, in most cases, they'll work. Everybody here knows somebody who's taken a "side-hill salmon" with a .22 - we all know that if you pick your shot you can drop a deer with your Ruger 10/22.
Well, a deer might weigh 150 pounds. A good brown bear weighs 1000 - 1500 pounds. Do the math - if you increase the weight of a .22 by 10 times you are approaching the scale of shooting a big bear with a 400 grain .45/70 slug - and at some little distance the velocities even match.
I know this comparison is perhaps a bit weak, but it gives you something to weigh the merits of shooting big critters with light rifles. If shooting a big bear with a .45/70 is "something like" shooting a deer with a .22, why would you want to scale that back even further?
Keith