No, I point out here that their logic is quite correct! The problem is not with their reasoning, instead it’s with their perception that everyone is out to get them, it’s with their premise.
And FWIW, it is also possibly (but perhaps unlikely) to reach a correct conclusion from faulty reasoning.
Quite so! You have perhaps seen the FarSide cartoon where a mathematician has put up a proof on the blackboard, where one step reads “And then a miracle happens…”
Or once I put up a proof for my math teacher’s challenge, and as I was presenting it, he said “There! You divided by zero.” And I had! But the challenge was to prove a true statement, only my proof was faulty, even though it got the right result.