This is a specific kind of Did Not Do the Research, where a pivotal clue in solving a mystery or puzzle is actually erroneous. This is related to Conviction by Contradiction, where a single thing wrong with an alibi is sufficient to prove guilt, but goes further: the key that makes the claim or alibi wrong is itself factually incorrect. Distantly related to Dan Browned, because if you're going to write a mystery and have the solution all hinge on one fact, the audience is fully justified in expecting that that fact is really a fact. Examples of Conviction by Counterfactual Clue include: