Why would he believe it and the DM not? If it's in his background, both should believe it. If it has come up in game play, both should believe it. If he's getting it from a skill, then the DM is determining yes, no or in doubt and both will believe the result. If it's based on consistent prior roleplay(firebolt in the first round of every combat), both are going to believe it.
That's not going to happen. The players are bright enough to know when something will need to be known before acting. Such as, oh, literally every monster special ability or defense ever.
No. No veto is ever happening. My telling you no, you can't bring in OOC knowledge is not vetoing a single action. Ever. To veto an action it has to be as the action is happening and then you being told no. That doesn't happen.
Edit: No,
@Lanefan is not espousing support for what you are talking about. Go look at post 955. He's talking about telling a player who is clearly playing bad faith that he cannot play in bad faith.