> Maybe it's a complete coincidence.
The word "correlated" means that it is NOT just a complete coincidence. One might not cause the other, they might be correlated because of a separate factor that interacts with both, but if they are "correlated" then complete coincidence can be ruled out.
> [...] So the lead is correlated to crime historically, even though neither causes the other directly.
Yes, this is what I mean by a third factor affecting both. But lead is a physical effect -- there are only certain sorts of things that can cause it. Things like eating lead, breathing lead, or having a diet that causes one to incorporate less lead into neurons. Thinking happy thoughts cannot change your lead levels (directly). So there are only certain categories of separate factors, C, that could be the cause of both A (lead) and B (crime). Where your name comes in the alphabet might conceivably cause crime, but it simply cannot cause lead. C, if it exists, must be a physical effect.
That's why I mentioned controlling for location where people live. That is a likely candidate for C: it is plausible to correlate with crime and it is possible to correlate with lead. If you control for it and still find an effect, then either A causes B, B causes A (not reasonable), or there is a different C'. Perhaps a genetic mutation that increases lead absorption and also alters brain chemistry to increase propensity to crime? That one is already a bit of a stretch.
I guess what I am saying is that it is true that correlation does not imply causation, but that there are reasonableness constraints on the kinds of interactions one can hypothesize, and after a certain point Occam's razor implores us to consider causation.