That does sound like a flaw, although the paper by Jessica Wolpaw Reyes I often see mentioned that argues lead causes crimes isn't based on measuring lead levels in individuals at all, but on the total lead released by cars during the time studied. That sounds even less robust.
I'm not sure if the paper you linked measures the correlation between blood lead levels in the first 3 years and crime rates because it's behind a paywall.
I wasn't aware of sci-hub, but it seems awesome. Thanks!
The paper you linked by Nevin seems to be doing the same thing as the paper by Reyes. They didn't test the lead levels in individuals studied, but looked at the total lead released by vehicles at the time.
I'm not sure if the paper you linked measures the correlation between blood lead levels in the first 3 years and crime rates because it's behind a paywall.