The characters have no reason not to trust Mr. White, but because the players know he's the bad guy, they go to great lengths to dig up evidence of his untrustworthiness. Communication - A GM's Best Friend Talk to your players. Some people don't know that use of out of character info is a bad thing. Maybe they played under a GM who allowed such things before they played with you. Or it makes sense to the players in the first example that if their friends haven't come back yet, something must be wrong, and thus they're justified in taking a more defensive stance as they continue.
Communication comes in several parts.
First, make sure your players know ahead of time that use of OOC information is considered off-limits, and why. Allow him to re-choose his actions. Note that this does NOT work if you don't tell him why you're doing it - you need to point out why you're docking his points. Fourth, if you're having a real problem with a player who just won't stop, then take him aside. Privately, tell him that what he's doing is considered cheating.