When I went kayaking and hiking in an Arizona wilderness a couple of years ago in an area inhabited by mountain lions and wolves (with no weapons on me except a small riverman's knife), I soon learned that the biggest threat to my safety was from the barbed-wire fences which crossed the rivers and trails.
I hear that hungry cougars tend to sneak up behind you and go for your neck, though, so the Canuck in the story was apparently very lucky and very determined to have survived.
By far, the greatest danger to people in remote areas are predatory humans.