Well I don't know about the way legend has it that Davey Crockett/Fess Parker did. Old timers had a saying about a persons foolhardy conduct. They use to say a person engaged in stupid stunts was "Goin' hunting bears with a hickory switch".
But before the Bowie Knife became famous and sometimes called the "Arkansas Toothpick", any large knife, such as the "rifleman" knife of longhunters fame, in Arkansas was called a "Bear Knife".
So who knows what they actually did with those things and I am sure that if a bear attacked you and your single shot rifle didn't stop the bear, of misfired, you defended yourself against its attack with your knife. That's the reason you carried a big one. In any case the wrong thing to do if a bear attacked was run because a bear will outrun you, and he can climb a tree pretty fast also.
So in those days hunting "Bears with a knife" meant that you stood your ground against the odds. And I would imagine that there were a lot of them old boys that did that.