Well, to be conservative, assume she was told or guessed that 7 out of the 12 samples were from patients with Parkinson's, which more than accounts for the "predisposed to thinking at least some" factor - actually it would make more sense to guess six, but that can only make the correct response less likely. Twelve choose seven is 792, so out of the 792 possible responses, she chose the single exactly correct one. No fancy statistics needed - the p-value (defined, according to Wikipedia, as the probability of obtaining an equal or more extreme result, the latter of which doesn't apply as the result is already the most extreme possible for the experiment) is simply 1/792 or about 0.001 (0.1%).