Everyone knows that there must be other primary factors that influence the rate of violent crime. Reason? The rates per population vary quite widely between places - the rate in Toronto is not the rate in New York, and naturally, this is the result of other factors - poverty levels, social infrastructure, race relations, etc. No-one claims that (say) Canadian cities used less leaded gas that US cities, so the difference between places can’t be caused by lead.
The graphs showing the correlation between lead use and violent crime show a good “fit” at (say) the city level. The implication is that, all other things being equal, it is lead that makes the difference in crime rates over time within each city. So, presumably, if Toronto has a much lower violent crime rate than (say) New York, that’s due to “other factors” - but the variation over time within each city is due to lead.
However, this would only make sense if all the other factors, which we know must make the majority of the difference between cities, remained constant over time - which simply cannot be true. The cities have changed, and presumably, in different ways.
Given that we know (a) that other, non-lead factors make most of the difference in crime rates, as evidenced by the fact that violent crime rates differ significantly between cities, and (b) that these factors do not remain constant over time, then (c) it cannot be the case that lead use would perfectly correlate to the increase and decrease of violent crime over time. Even assuming the theory that lead use had a significant impact were true, one would predict that it would be difficult to tease out the data from the noise cause by the other factors.