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But their paranoia has absolutely no bearing on whether or not they are being followed. It's all just unassociated coincidence.

You cannot look at their paranoia and conclude from it that anything else is going on, so as a fact it has no significance. In order to determine causality you need objective, verifiable, and reproducable evidence of cause and effect as well as a logical hypothesis for confirmation. Ideally, it should be one that makes direct refernce to some other externally proven fact.

This story has none of that. It has nothing but a bunch of people that all saw a duck.

But there is evidence, or at least, there is what appears to be evidence (that's what needs to be investigated)...the mercury content in the vaccines.

To use your illustration, if it turned out that 90 of those 100 people were pooped on by the ducks they saw, would you not say there is possible causation there and that maybe it ought to be looked into? At the very least, a good scientist or debater would not overrule it without first disproving the possibility of the causal relationship. I'm sure if the vaccine-autism link is confirmed, it will include another undiscovered factor (weakened immune systems, for instance).

That's why we investigate, objectively, to determine if there is a cause-effect relationship.

My original comment was more against the casual citing of logical fallacies in an effort to undermine someone's argument. I see it more and more on FR and it's irritating to anyone who has studied formal logic. It doesn't further anyone's journey to the truth to shut them down with a line that sounds good.

The logical fallacy of equating correlation with causation is intended for an argument closer to what you presented, or something like of 100 traffic deaths on a given day, 90% were smoking and therefore smoking leads to death (it's a fine line between the false-cause and correlation-cause fallacies because they have similar roots), not in the case of a possible link between autism and vaccines, where there are strong possibilities of a causal relationship (the mercury).