no, people are mostly terrible at perceiving actual risk vs. the imagined, because evolutionarily, it was much less harmful to get it wrong one way than the other. we humans no longer live in a world of such unpredictable mortality. and even if imprecise, statistics provide relevant information, especially on relative and general magnitude. moreover, serious crimes are the ones most likely to be reported, and therefore having more accurate stats, so survivorship bias isn't a significant factor.
humans consistently overestimate the dangers of the unknown and consistently underestimate the dangers of the known, often by orders of magnitude. we're also wired to be highly overconfident in our estimations of just about anything. your conjectures include prime examples of such mis-estimation, e.g., "much greater risk" and "hundreds of times more dangerous", implying all that avoidance behavior is justified. but death by firearm, for instance, is caused 90+% of the time by the self or familiars, yet we spend all of our time and resources worrying about strangers and extremely rare scenarios (armed robbery, home invasion, mass shootings, terrorism, etc.) rather than the common (suicide, accidental shooting, crimes of passion, etc.). mostly, we worry about the wrong things most of the time.