A good way to avoid this conundrum is to ask questions that are worth solving in real life.
If the candidate breezes through the discussion because they've actually had to solve the problem before, then their victory is well earned.
If on the other hand its an academic question in the same vein as the data structures or algorithms puzzles you find on $interviewprepforum, then the fact that they've solved it before tells you very little.
I don't think there's much difference either way. In both cases, a candidate gained a large advantage in a way that tells you very little about their ability.
I think this is why contrived questions gained popularity in the first place - they eliminated noise due to candidates randomly having solved similar problems before (that and "real life" problems usually can't be explained and solved in 1 hour).
I think this is on the right track. The best interviews I've been a part of involve the interviewer asking a question they don't fully know the answer to. Then the interview turns into a conversation where both parties are trying to work together to formulate an answer. The candidate should be scored based on how constructive that conversation is.
If the candidate breezes through the discussion because they've actually had to solve the problem before, then their victory is well earned.
If on the other hand its an academic question in the same vein as the data structures or algorithms puzzles you find on $interviewprepforum, then the fact that they've solved it before tells you very little.