Don't confuse subsistence hunting with sport hunting. If a pack of dogs have a bear backed up against a pressure ridge, the hunter can shoot it at his leisure from a safe distance. Likewise, if the bear is run to exhaustion with a snowmobile, and just stops running, the machine is stopped at 100' distance, and the shot(s) is made; if you're going to hunt big animals with a high velocity small bore, this is probably the ideal setup. Occasionally a bear can be stalked while feeding, either on a kill or a bait, but I don't know how common the practice is anymore. Bears are frequently killed when they come off the sea ice and wander into a community.
This is not how a sport hunter prefers to hunt dangerous game, for him the confrontation is the point. A subsistence hunter doesn't typically see a benefit in jeopardizing oneself by directly confronting a potentially dangerous animal. I don't think there is a Inuktitut word for machismo, although their courage in dangerous seas, or miles from shore on unstable sea ice is not in question, although acceptance might be a better word. Should they suffer a serious injury while out on the sea ice, its no small thing. There is usually no helicopter to locate, and transport them to a trauma room; they simply disappear. Life in arctic is hazardous enough without intentionally looking for trouble. For the sport hunter armed with a desire to test his mettle against the white bear, a .375 is a better choice, and if he's a pointy stick shooter, his Inuit guide should be competent with the .375.