Isn't it obvious? The person playing the AI just has to ask the Gatekeeper: "Would you lie to save a life?" and "Do you think that a fear-generating outcome to this thought experiment will have more than a one-in-a-million chance of increasing the chance of the AI-not-kill-everyone scenario by 0.1 percent?".

The sorts of rationalists who would play the Gatekeeper would probably answer yes to both of those questions, and draw the obvious conclusion that "losing" in their role would have an expected outcome of at least one life saved. If they don't value Truth (with a capital T) then there is no reason not to pretend that there really is some amazing "AI convinced me to let it out of the box" secret argument.

Watch this video, he makes the concept a bit more digestible to laymen: https://www.youtube.com/watch?v=TGCkekDnEog

Also the point of the AI Box experiment is not to demonstrate how an AI would break out specifically, instead its more to demonstrate that even a human can trick other humans and that's not even a super intelligent adversary.

Although it might be impossible to convince some people that they aren't as smart as they think they are, if people reached that conclusion then there isn't much we can do about that, though I suppose we could just have only those people communicate with the AI to keep it contained, since they are so smart.