But the only RPG I can think of which sits on the chess side of your example is 3E D&D and its cousins, or very vanilla combat encounters in a rules-heavy RPG like HERO, 4e D&D, RM, RQ, etc.As I mentioned upthread, trust might not be the most accurate word for what they are trying to describe. To me what they are trying to describe is what the table references when there is uncertainty. So if you are playing chess, there are clear legal and illegal moves. If you are learning how to play, you can reference the rules and see a pawn can only move forward, or diagonally to replace an opponent's piece. So in that sense you have "trust" in the rules: as long as we follow the rules the game will be fair. "Trust" is not about your chess opponent not cheating, though incidentally it's easier to verify whether they are or are not. Free Kriegspiel wargames, to my understanding, replaced the rulebook with a referee. So now instead of "trusting" the rules to adjudicate your position and actions, you "trust" the referee.
Consider AW. Your PC goes aggro and gets a total result of 5. Now the GM can make as hard and direct a move as they like. What should they actually say? I've played with plenty of GMs who I wouldn't trust to GM AW, not because they're cheaty types without integrity but just because they don't have a good imagination for dramatic fiction.
I did offer some conjectures about this in the OP.So for Kriegsspiel referees, the foundation for trust is established. They are trustworthy because they are experts in the area, they are not invested in seeing a particular side win, and they are ruling about a scenario that has been established with minimal input/design from them.
What would be the corresponding factors that would serve as a foundation of trust for a FKR GM?
In S'mon's response to the helicopter problem we got say 'yes' or roll the dice as a way of plugging gaps in expertise.