I haven’t read the paper, but I wonder how well they control for economic status. I’d expect the better off a family is the less lead they have in their life - and I’d expect economic status to actually be a cause of better education, health, incarceration, etc.
They said “we compare outcomes for children who are similar across observable characteristics but differ in eligibility for intervention due to blood lead test results.” Economic status is observable, so ide guess it’s I caused; but I only read the abstract.