I don't think the "over-fitting" problem applies to the Turing Test: you can ask the candidate about anything, and adapt your later questions accordingly. There are proofs in computational complexity (that I'm too lazy to look up right now) that show that you can't pass this kind of test (except with exponentially small probability) but by containing a polynomial-time algorithm for the entire problem space. (It's related to the question of what problems are IP-complete -- i.e. the hardest among those problems that can be quickly solved via interactive proof.)

It would only be analogous to the test of the students if you published a short list of acceptable topics for the TT and limited the questions to that. Which they don't do.

Edit: If you were right, it would be much easier to construct such a "conversation savant" than it has proven to be.