It is not incorrect information that you are trying to prevent! The proof checker ensures that the result you get is correct. What you want to prevent is correct information which has all of its degrees of freedom besides correctness optimized against you. You do that by taking away all degrees of freedom besides correctness, using this procedure.
The deception in the relevant sense here is when the genies conspire to give you an answer which retains all those degrees of freedom, and knowable incorrectness of an answer consists in someone noticing that the genies could, in fact, choose a shorter answer.
It is not incorrect information that you are trying to prevent! The proof checker ensures that the result you get is correct. What you want to prevent is correct information which has all of its degrees of freedom besides correctness optimized against you. You do that by taking away all degrees of freedom besides correctness, using this procedure.
The deception in the relevant sense here is when the genies conspire to give you an answer which retains all those degrees of freedom, and knowable incorrectness of an answer consists in someone noticing that the genies could, in fact, choose a shorter answer.