Interesting. It’s not clear that conspiracy theorists would disagree with scientists about the quality of an argument that touches on neither of their domains. It’s entirely possible that both are able to agree about good and bad arguments for (say) abortion rights, even if they have opposing positions. (E.g., they may well be able to agree that “X is a better argument than Y”, even when one disagrees with both, and the other agrees with both.)
We've been thinking about explanations in our research (see, e.g., https://arxiv.org/abs/2205.07938) and your example of explaining the wrong answer well is lovely.
I dislike these kinds of questions, because they're usually posed at a point well before the wave equations are presented. At this point, you are largely working with verbal explanations and, as you point out, verbal explanations are much harder to pin down.
Mathematically, if A implies B, and you are working to the best of your ability, you can't derive ~B (you may not be able to derive B, of course!) Verbally, this is not so clear; a lot of philosophy is people arguing about whether A implies B or ~B.
If the underlying logic is (as it is in physics) mathematical, then a verbal account of mathematical fact A can be loose enough that you can derive ~B, because the verbal account is also consistent with A', which implies ~B.
In these explanations, there's another factor: a lot of the talk is relying on intuitions for "ordinary solids". One explanation I encountered when I googled referred to the "stiffness" of a hotter gas. While you might be able to cash this out in more formal terms, the temptation is to think about stiffness in one's normal experience. (It might have been possible to get the right answer by imagining heating up a bicycle tire that's already inflated; intuitively, the casing will be stiffer, "ring" at a higher frequency, etc.)
If you continue on in physics to relativity, quantum mechanics, etc, you end up dropping this kind of talk very quickly. This is why I don't like these questions; it's a bit useless to get good at them, because the more advanced you get the more you learn to rely on mathematical intuitions to get the right answer (and then perhaps informal folk talk afterwards, if you communicate to a popular audience.)