Growing up around guns doesn't necessarily equate to knowing how to handle them, nor does sitting thru a hunter safety course make you safe. It's all about your habits.
In any activity, once safety becomes a habit and not just something you demonstrate when other people are watching you, the potential for injury becomes minuscule.
People who think they can be self-taught in learning to fly a plane are statistically more likely to die in a plane crash than someone who goes thru flight school, and learns habits like how to do a walkaround and follow a takeoff checklist...
Thru Scouting, I've been involved to varying degrees with youth shooting sports for 14 years. We don't just teach safety, we drill safety over and over until it becomes habit, e.g. always handling a firearm as though it is loaded (e.g. never believe someone when they say "Don't worry, it's not loaded...").
We're fortunate -- I've yet to see a gun related injury involving any of the hundreds of kids brought out to the range. I've seen some careless adults out at the range, but they don't last long before one of the rangemasters steps in and corrects them.