What I do think is that the degree to which a game (and by game, I mean the thing happening at a particular table, not an edition) can be about "player skill" is entirely a function of the GM's willingness to present his "puzzles" in good faith.
You are absolutely coming straight in with the a very insightful analysis! Yes this is absolutely key to "player skill". I don't think it's entirely that, but it's a big part of it.
Another aspect is the DM being reasonable and willing/able to listen to what the players want to do, and to think about it in an open-minded way, rather than being either skeptical, difficult, or just being slightly thick. Like, if your DM isn't very imaginative, and perhaps not the sharpest tool in the shed, and especially if he doesn't realize this, that can pretty harshly limit player skill, because he might not be able to deal with complex or off-the-wall plans. Now, it is rare to find a DM like that, but I have encountered a couple, and it was... an issue. Not even for me really because in both cases I wasn't the plan-having player.
Like, why would somebody build in a stinking cavern system a marble floor that becomes icy and slants towards twirling blades. Its sort of a long stretch of the imagination why this particular challenge even exists, until you realize the challenge is the game and the nature of its existence doesn't really matter in the grand scheme of things.
You say it doesn't matter in the grand scheme of things, and if it's a one-off, or a like, one-in-twenty sessions kind of thing, I agree with you.
However, if you start seeing that kind of thing regularly, I think tends to indicate what I find to be one of the most quietly hard-to-work-with kinds of DM. The kind of DM who
just never thinks things through. Who never bothers to consider internal logic and internal consistency within his world. One week sure, it's just a weird trap in a weird place and it's kind of odd because the DM himself doesn't seem to fully understand how the trap works, or maybe doesn't understand really basic physics (like that water is basically incompressible) involved in the trap, that it relies on. But next week it's a major NPC who the PCs are supposed to get on-side, but the DM has decided it'd be cool if the NPC was a massive jerk, and then forgotten to give that NPC any y'know, motivations or goals for the PCs to interact with, forgotten to make that NPC actually a person, and not a just a cardboard cut-out who sneers at and insults PCs for no apparent reason.
And I think this kind of DM is the one who has some of the most difficulty handling any kind of "player skill" in the sense players having good ideas or plans or schemes or whatever. Because his world is just random bollocks that he thinks is cool, and there's no internal consistency, he's likely to just reject player plans unless you accidently happen to do what he thinks would be a good idea (which is often something fairly strange - c.f. the whole "Eat the random food you found in a dungeon in a position that makes it look like an obvious trap and where nothing signposts that it isn't" deal discussed a lot a few weeks ago - to be fair that test was designed with internal consistency in that the DM understood the mechanism, but even then his expectations were unreasonable). And "random bollocks that seems cool" is a particularly big problem when the NPCs are like that too.
(The very worst and most cargo-cult form of this I've seen if the kind of DM who just has literally 95% of NPCs to be unpleasant, rude, hostile and just generally nasty to the PCs for no reason, and with no relationship to the personality, status, etc. of the NPCs, which is beyond just "random bollocks" and into something more obnoxious.)
This is something I've seen in actual games before too - I tend to avoid playing in any game where the DM is "like that" now. I think it's kind of fine when you're 12 or w/e, but when the DM is 35 and being like this? Well, you need the right group of players to go with that! With the right people, people who love random naughty word and don't like to come up with logical or careful plans as much as throw crap at the wall and see what sticks (which, to be clear, can be a lot of fun in the right circumstances), that sort of DM can excel.
It's not bad faith to be clear, either - these sort of DMs often mean well, but they're just not good at dealing with any kind of plan that y'know, makes sense or relies on internal logic/consistency.