Well fact can be true and untrue. In todays world, most people consider somthing true a fact. Which ironically is of course a false fact. I see alot of legal people will state somthing untrue with "false factual statement." I would add a "'s" if the person was a total believer in false facts.

Also here is a excerpt from synonym.com: "delusive, false -- (inappropriate to reality or facts; "delusive faith in a wonder drug"; "delusive expectations"; "false hopes")"

So it could work as in: "He delusively chose A."

~Ari I'm not that smart, but I might be right.