The issue is not blind faith in a rule -- though many safety rules should be simply followed always, unerringly -- but mitigation of risks.
A fence, ditch, stream, etc. has been identified as a particularly hazardous moment in a hunter's travels, and unloading the gun to cross them is a simple and effective way of eliminating one serious risk with a universal catch-all solution. That's fine. Certainly no argument about the effectiveness of the solution.
But hunters don't generally walk down paved sidewalks all day -- the natural world is full of trip hazards and slick spots. And game may be encountered anywhere along the way. So unloading your gun when you're near unsure footing becomes a near-constant condition, possibly precluding taking the shot you came out here to get.
Also, while completely unloading a gun is a simple and utterly effective way to make any and every firearm safe, it is unnecessarily overboard. Just about every firearm I can think of has some method of disabling the firing mechanism with a simple operation, so that the gun cannot possibly fire -- without actually unloading it.
Bolt gun? Raise the bolt handle and retract it 1/2". Gun is dead in your hands.
Lever gun? Lower the lever, even eject the chambered shell if you want. Gun is inert.
Break-actions? Crack it open.
Pump? Rack it back and pocket the empty.
Falling or rolling block? Open the action.
Semi-auto? Lock the action open.
Or...if you like to live on the edge, just put the safety on. Dollars-to-donuts, every single near- or tragic accident of this type the poor soul who's gun went off did not engage the safety. There simply aren't that many safety failures in the world, and the combination of a safety device being swept off AND the trigger depressed simultaneously by sticks, twigs, or other detritus are simply astronomically remote. Why do these things happen? I'd bet my last dollar the safety was not engaged, and my last 50 cents that the "twig" that pulled that trigger was really a finger that managed to be not quite outside the trigger guard.
(But he said the safety was on, his finger was up his nose at the time, and the gun just "went off?" Go figure ... I'm sure that's what happened.
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I'm not casting stones at anyone here, or those they've known who had this happen, BUT. I've made mistakes of my own in my life, and I've known a lot of hunters, and between the two ... that's my opinion on accidental shootings.
But, based on that opinion -- if we can't trust shooters/hunters to remember the safety rules about keeping muzzles pointed in safe directions, and can't trust them to keep their fingers off of triggers, and can't trust them to apply the safety when not actively shooting -- why will they magically remember (and practice) going through such an involved routine of unloading completely and reloading a gun every time they come to uneven ground?
Accidents are always going to be with us. But not because folks didn't take the most extreme or complete steps to render their weapon safe. These things happen because folks forget or ignore the very most BASIC safety steps.