You redefine syncophancy too narrowly. Many (if not an outright majority of) everyday LLM users have neither the educational foundation nor skill to ask good, well-formed questions like the one you propose. We should consider syncophany in the scope of an average person's non-optimal use of LLMs. CrazyStat's prompt is something your average Joe will absolutely feed an LLM, and Joe will walk away with something very much like those plausible falsehoods. We have to think of and work against LLM syncophancy in the scope of how the hypothetical average person will use an LLM.