the impossibility of arriving at A-->B<-->C for this example from any existing algorithms for deriving causal structure from statistical information.

Correct me if I'm wrong, but I think I already know the insight behind what you're going to say.

It's this: there is no fully general way to detect all mutual information between variables, because that would be equivalent to being able to compute Kolmogorov complexity (minimum length to output a string), which would in turn be equivalent to solving the Halting problem.