I'm a different AC, but I think you made his point. "You are unlikely to see another human being for days" in those hundreds (is it really thousands?) of square miles precisely "because practically nobody lives there or will ever go there."
Yes, I did. I also made the point that his point is irrelevant. We're talking about a minuscule proportion of the population. It's not that their wishes should be ignored, exactly; I believe that creation and protection of rights is a valid pursuit. But "It is virtually impossible for people to not run into each other," is still a completely valid statement. Virtually nobody lives in a situation where they won't see other people. Someone always turns up, if only for a sample of something. Maybe you. And frankly, there really is nowhere like you describe in the USA, either. There's a number of large private ranches of thousands of acres; those guys often have stories of trespassers. And a large portion of the country is owned by the Bureau of Land Management, which regularly portions big sections of it off for military and police training, and which patrols it regularly and investigates fires, target shooters in hunting season and hunters out of season, and the like. Then there's the big state parks, which are full of state park rangers on horses and in Jeep of various types, and IIRC Chevy trucks. They manage to cover quite a bit of ground.
So yes, it is virtually impossible to not run into people. You have to go to significant lengths, especially since people are actually looking for people in those supposedly empty places. Sure, you could get lost in the asscrack of some mountain somewhere, but even getting there is beyond the reach of many people. Only a tiny slice of the world population even lives away from someplace where you can avoid seeing people for more than a few minutes at a time.