The rulebook quote is hilarious to me, because I cannot count the number of times I read a Pathfinder Society scenario that had different DCs for each different level band.
The catch is, the world IS going to scale by the very nature of wanting to present challenges.
You present the challenge of having to balance on a log at level 1. If you want to do so again a few levels later, you're doing so because you, as the DM, want that element in the game that brings with it a chance of risk and failure. You're never going to throw the level 1 log task at a 10th level party because it's not worth the time it takes to roll. You just say they auto-pass and move on.
Balancing on a log has become "tie your shoelaces" or "climb a ladder" or "start a campfire in ideal conditions" in that it's a task you're not going to bother asking for a check for, as there's no reasonable chance of failure.
As the DM, if you want that kind of element to the encounter, then it will be artificially made more difficult. If you want to have the level 5 party challenged by crossing a log (either as an exploratory challenge or as a bit of terrain in a combat encounter) then it's going to be a hard to cross log. It's going to be slimy and its bark is sloughing off. Otherwise... what's the point? They wouldn't even get experience for it.
And because you want to keep doing different things and not running the same encounter again and again, it's unlikely players will encounter the same task in short order. You've had that encounter, you're going to do something different. So there's not likely to be many times you come across a challenge at level 1 and then encounter that exact same challenge at level 4 and can bypass it with ease, because the DM already run that challenge and wants to do something new and different. "Gee, I ran a greased log over a gorge encounter at level 5. Why would I do it again at level 8? It's going to be loose stones on a river of lava."
Plus the "checks against opponents’ DCs, higher-level adversaries have higher skills, so the players can clearly see improvement as they challenge and surpass more powerful foes" bit is kinda B.S.
You had a 50% chance of hitting the goblin you fought at level 1. And then at level 10 when you're fighting the goblin archchief, you still have that 50% chance of hitting. There's no real improvement as the monsters level with you. You don't see an improvement, the numbers are just bigger. You can replicate that same effect by just remaining at level 1 the entire game and describing the enemies as bigger and scarier.
