I think Carrot is a great example of the type of dramatic irony you're talking about here. For those who are unfamiliar with him, he's a character in Sir Terry Pratchett's Discworld series, which is a comedic fantasy setting with wizards, witches, elfs, dwarfs, etc. Among other things, Carrot is a six-foot-tall dwarf. This is funny.
The humor in Carrot relies on multiple pillars of comedy, the first of which is that a joke must be based on something both the comedian and the audience agree is true. In this case, the thing we know to be true is that dwarfs are short. Anyone who enjoys fantasy fiction and thus would be likely to read a Discworld book knows this. The author also knows this, and we trust that he knows this because he demonstrates his deep knowledge of fantasy writing tropes at every turn. Thus, when Sir Pterry talks about a six-foot-tall dwarf, we know he's deliberately subverting the trope, and it's funny. If he didn't know what he was doing, and just declared that he can have his dwarfs be six feet tall if he wants to, it wouldn't be funny; it would be stupid, and people would reject it for more or less the same reason people reject (and make fun) of Twilight's sparkly vampires.
But it doesn't stop there. Another pillar of comedy is surprise or contrast: a sudden, sharp difference between one state and another. It's not just that Carrot is tall for a dwarf; he's even tall for a human. He's absurdly tall for a dwarf.
And then there's the dramatic irony: a situation where the audience knows something the characters don't. See, Carrot is, in fact, biologically human! But he doesn't know that, because he was raised as a dwarf, by dwarfs, and is therefore (in Sir Pterry's world) so literal-minded that he never questions this until his parents reveal the truth to him.
He still thinks of himself as a dwarf, though, and culturally he still is, so the fact remains that he is a six-foot-tall dwarf. {= )
The point is, it's not funny because he's tall. It's funny because everyone knows dwarfs are short, and he's absurdly tall, and he's actually not biologically a dwarf at all, and he has no idea even though everyone else does (which is consistent with his ongoing characterization as literal to a fault). The humor comes from all these layers of comedy rolled together by a writer who knows exactly what he's doing. And that—the ability of a comedian to create a rapport with the audience—that's a really important ingredient in the mix. (Meanwhile, Sir Pterry is always sure to write characters who are like actual people, if somewhat exaggerated ones, with consistent motivations and personalities that evolve in ways that make sense in response to their experiences, but that's a slightly different discussion.)
I write all this so that it will hopefully make sense when I say "they're stupid and wrong" by itself is not a joke, just like "Carrot is tall" by itself is not a joke. Good comedy takes a lot more than that, starting with a shared understanding of what's true and what's not. Without that, it will never work.
~Neshomeh is not fit to kiss the brim of Sir Pterry's hat, but fancies she has learned a thing or two about writing comedy from his most excellent example. RIP, Sir Pterry.