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.
A friend has been asking my views on the likelihood that there's anything to a correlation between changing levels of lead in paint (and automotive exhaust) and the levels of crime. He quoted from a Reason Blog:
I responded with the following:
He's apparently continued to pursue the question, and just forwarded these remarks from Steven Pinker that I thought were very illuminating, and probably deserve a place in this community's toolkit for skeptics. Pinker's main point is that the association between Lead and crime is a long tenuous chain of suppositions, and several of the intermediate points should be far easier to measure. Finding correlations at this distance is not very informative.
http://stevenpinker.com/files/pinker/files/pinker_comments_on_lead_removal_and_declining_crime.pdf
Does the phrase "long-chain correlation" stick in your head and make it easier to dismiss this kind of argument?