Ill be the odd ball here.
Depends on the kid. Some kids are overly cautious. My daughter is a very study child. athletic and can do most anything. She absolutely will not try anything though. Ive had to force her to do everything that she now loves. Shooting wasn't one but riding an ATV. Driving a Car, Then driving a stick, riding a roller coaster, hell eating Japanese food was a big fuss. Lol. Now it's her favorite thing. She absolutely will not try things. I tell her try it and if she hates it then never try again. But try it. She loves playing basketball. Me and my friends rented a gym and played ball for years. I had to force her to play ONE time. She has finally (at 12) realized that if I tell her she can do it, she is safe and can try at least.
The roller coaster was at a huge theme park. I despise roller coasters myself. I panic on roller coasters with Scooby-Doo on them. The log flume makes my heart skip. (I also raced sportbikes and cars, 200+ doesn't scare me on a track at all. On quads and dirt bikes I was the idiot you see jumping cars and such.... 3 mph on a rollercoaster I have no control of...full on panic. Heart stops, I sweat.... no good.). I worked on getting her to ride a kiddie coaster (with me) for half the trip. Once she did though, she rode everything. Still loves it.
We have a great relationship too. I'm closer to her than my other two. We have most everything in Common. So I believe it depends on the kid. A good parent knows when to push and when not. Sometimes they don't think they are strong enough or ready. Sometimes they think they will let you down and are terrified of that
My other two have very little fear or caution. Even if they want to do things I have to decide of they are ready, because according to them....they are ready.
The father in the story may be a huge A-hole and making a mistake. But he may know that if the kid shot the gun (in a lead sled, not like the morons handing a 95lb woman who has never shot a gun a 338-378) that he would be confident and be ok with it.