> conversations usually start with claims that are hard to believe, and completely unsubstantiated. Like Occam's Razor points in the complete opposite direction. Requests for evidence to back the claim up are usually deflected

In public, you just have to put a stake in the ground as delicately as you can. Something like: "All our research showed that A is the best way to go. We have not seen this data that B is better, so we continue to recommend A." At least then baseless assertions aren't standing entirely unchallenged.

Privately, you may be able to gently escalate the issue... Reminding Mr X's boss or another interested party that you never received the information Mr X promised, and hint at your doubts of the veracity of Mr X's claims.

> it's then applied in a non-sequitur argument of "unsubstantiated claim A, so we should do B" where there's no logical reasoning that A should lead to B.

Any chance Mr X is very familiar and comfortable with "B", and much less with "A"? I have seen this kind of behavior with some people, who don't want to put in the effort to learn something new, or are deathly afraid looking incompetent. The result can be an extremely unpleasant personality.