People do get attacked. I worked or years with a fellow NPS employee who was attacked by a grizzlie while on duty - she played dead, but her companion was injured. So it does happen, at least in Alaska.

But problems due to wild critters are not that prominent in the overall hazard profile one faces when going outdoors. Statistically, the Jaguar you drive is more likely to do you harm that the cougars out in the woods, to say nothing of problems created by microbes, falling, weather extremes, and drowning. Those are the things that really pose a problem.

Wild animal encounters make a big splash in the media when they occur, while more common problems are not emphasized, if mentioned at all.

Personally, the only time I have visited an ER for an outdoor injury was the result of a fall while rock climbing - no problems with critters whatsoever.