I just read in Goswami's book (page 21) that Turing himself admitted that psi would be a way for a machine to fail the Turing test. The following quote is from "COMPUTING MACHINERY AND INTELLIGENCE" http://www.loebner.net/Prizef/TuringArticle.html where Turing addresses the "Argument from Estrasensory Perception":
I assume that the reader is familiar with the idea of extrasensory perception, and the meaning of the four items of it, viz., telepathy, clairvoyance, precognition and psychokinesis. These disturbing phenomena seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming. It is very difficult to rearrange one's ideas so as to fit these new facts in.
Turing wrote, "If telepathy is admitted it will be necessary to tighten our test up." He would have to devise some "telepathy-proof room" assuming that were possible. Perhaps the best way would be to not allow any questioning that tested for psi ability.
Since we discussed the Turing test earlier, I think this argument by Turing himself is better than Searle's Chinese room argument I used earlier.