Well, see, that's the whole deal, investigating _how_ different it is than flipping coins. That's the whole question, really. Starting with the assumption that they _must_ be doing better than chance is not the right place to start in order to analyze if they are or not.
Most statistical analysis is about trying to distinguish meaningful results (implying a repeatable correlation of some kind that means something), from random chance with no meaning. The whole point is you _don't_ start out knowing if the thing you are investigating is random chance or not, if you did, you wouldn't need to analyze it. That's what statistical analysis is for. In part because we humans are really really good at finding patterns and assuming a meaningful correlation when in fact it's just random chance.
The coin example is useful because we all know (or define for the sake of the discussion) that it must be random chance, so any analysis that appeared to say it wasn't is probably in error. And using the same sort of analysis on something where you don't know how much of the effect is due to random chance--is not going to answer the question.
