It is widely understood that statistical correlation between two variables ≠ causation. But despite this admonition, people are routinely overconfident in claiming correlations to support particular causal interpretations and are surprised by the results of randomized experiments, suggesting that they are biased & systematically underestimating the prevalence of confounds/common-causation. I speculate that in realistic causal networks or DAGs, the number of possible correlations grows faster than the number of possible causal relationships. So confounds really are that common, and since people do not think in DAGs, the imbalance also explains overconfidence.
I'm pointing out that your list isn't complete, and not considering this possibility when we see a correlation is irresponsible. There are a lot of apparent correlations, and your three possibilities provide no means to reject false positives.
You are fighting the hypothetical. In the least convenient possible world where no dataset is smaller than a petabyte and no one has ever heard of sampling error, would you magically be able to spin the straw of correlation into the gold of causation? No. Why not? That's what I am discussing here.
Full article: http://www.gwern.net/Causality