It could still be bayesian reasoning, but a much more complex one, underlaid by a lot of preconceptions (which could have also been acquired in a bayesian way).

Even if the result is random, a highly pre-trained bayessian network that has the experience of seeing many puzzles or tests before that do follow non-random patterns might expect a non-random pattern... so those people might have learned to not expect true randomness, since most things aren't random.