I think "lead paint causes crime" is evaluated based on direct mechanisms of brain damage, behavioral changes, and somewhat controlled population studies.

This known mechanism is then offered as a dominant causal mechanism for historical crime rates based on their correlation to time lagged lead exposure rates.

It's a perfectly reasonable way to try to explain historical crime rates. What it would not be is a reasonable way to establish that lead exposure induced crime, which I think you mistake the procedure for.

The threat of confounders is inevitable in population studies, but that doesn't mean you don't do historical population modeling.