I think the actual sequence of events is more like this: crime rates fell drastically all over the US starting in the very early nineties. It's not often in social science that a phenomenom cries out for a causal explanation with a single overriding cause, but this was one such.

The time-lag of the correlation provided enough evidence to bring the lead hypothesis out of the "epsilon probability" regime. That's straightfoward Bayesian reasoning -- verifying a consequence (i.e., prediction) of a hypothesis increases the plausibility of the hypothesis. Further predictions of the hypothesis were then verified -- things like prospective longitudinal studies showing the association of blood lead levels and violence on the individual level and natural experiments generated by the slightly different timings of various countries' and various US states' lead gasoline phase-outs.