The rules of the game don't require truthful answers: "I don't know" can always be uttered in response to any question. A strict epistemological nihilist (skeptic) must answer all questions with "I don't know": the opposite of such an epistemological affliction, which doesn't have a conventional name but we could call him an omniscientist, can never truthfully reply "I don't know". Similarly, which conjoined with an explanation of Aristotle's first principle of logic, the sentence that ends "and do you agree that those who deny the first principle should be flogged or burned until they admit that it is not the same thing to be burned and not burned, or whipped and not whipped" can't be answered "I don't know".
Perhaps you have in mind that lying, being uncooperative, or being a skeptic, is proof that a person is unhealthy, so maybe you should first define "healthy".