In fact, with many accidents, it's often a matter of compounding mistakes. (The victim didn't have a lot of experience, went out in worsening weather, lost the trail, and didn't have the gear to survive overnight.)
On the other hand, it's easy to identify "mistakes" in retrospect. Someone got caught in an avalanche so they "clearly" shouldn't have been somewhere that they could get caught in an avalanche--even if the danger was just moderate and the danger in that particular area is often moderate.
Which also speaks to your statistics comment of course. There are various levels of danger to many activities and you can reasonably reduce your chances of something going wrong but not eliminate them.
And, also of course, many people who don't participate in many of those activities see them as unreasonably dangerous. And, depending upon their political views, may think rescuing mountain climbers or even winter hikers as a waste of societal resources.