You would be up a creek with a 243 or 270 out deer hunting and a grizzley comes around. Fortunatly these are pretty much little 400 poundish black bears. No Daniel Boons here.
Good thing that there is no 9 foot tall 1000+ pound grizleys around, they are not cuite or cuddly and would be hunted into extinction again.
Think of it like this, If you were in the water you wouldnt want to see a shark.
The bear like the shark could eat you if it wanted and there is nothing that you could do about it. NOTHING. It is the largest predetor that we have to worry about besides mountain lions. Fortunately for me Im on the other side of the state were there are non. Just the big kittys.
That's probably why they don't use 243's in Alaska... A mountain lion has just a good of a chance to get you as these big dogs they call black bears here. You are just being paranoid, the number of grizzly attacks vs people roaming Alaska is minute. Just be glad we don't have tigers here...or 70% HIV population