I'm choosing to ignore that possibility to clarify the exposition of what I think is going on. Problems like that are what I'm referring to when I preface:

And we can't explain all of this away as the result of illusory correlations being throw up by the standard statistical problems with findings such as small n/sampling error, selection bias, publication bias, etc.

Even if we had enormous clean datasets showing correlations to whatever level of statistical-significance you please, you still can't spin the straw of correlation into the gold of causation, and the question remains why.

You could say that "A and B happen to be in sync for a while" is possibility 3, where C is the passage of time. (Unless by "happen to be in sync for a while" you mean that they appear to be correlated because of a fluke.)