Poverty is easy to control for. Controlling for it brings the Pb-IQ effect size down considerably, but not down to zero.
My view is that poverty, low IQ, and lead exposure are all caused by intractably complex webs of genes, behaviors, beliefs, and parenting styles. This occurs in such a way that high IQ, high socioeconomic status, and low lead exposure are all strongly correlated, but not perfectly correlated.
As a spherical-cow sort of model, imagine that there's a "I don't give a fuck" (IDGAF) gene. People with the IDGAF gene have higher levels of lead exposure (because their houses aren't as clean), lower IQs (because they're not as motivated to think hard about the IQ test problems), and lower socioeconomic status (because they're not as motivated to get high-paying jobs) relative to those without the gene. But some IDGAF-positive people will get lucky and end up with high-paying jobs. Some IDGAF-negative people will be impoverished due to bad luck, etc. In other words, socioeconomic status is a noisy indicator of IDGAF. The key point is that IDGAF-positive people who have good jobs still probably don't keep their houses as clean as IDGAF-negative people. So when you control for poverty, you've killed off most of the IDGAF-mediated correlation between lead and IQ, but not all of it.
(as a reminder, this was just a spherical-cow model for illustrative purposes... reality is intractably more complex!)
My view is that poverty, low IQ, and lead exposure are all caused by intractably complex webs of genes, behaviors, beliefs, and parenting styles. This occurs in such a way that high IQ, high socioeconomic status, and low lead exposure are all strongly correlated, but not perfectly correlated.
As a spherical-cow sort of model, imagine that there's a "I don't give a fuck" (IDGAF) gene. People with the IDGAF gene have higher levels of lead exposure (because their houses aren't as clean), lower IQs (because they're not as motivated to think hard about the IQ test problems), and lower socioeconomic status (because they're not as motivated to get high-paying jobs) relative to those without the gene. But some IDGAF-positive people will get lucky and end up with high-paying jobs. Some IDGAF-negative people will be impoverished due to bad luck, etc. In other words, socioeconomic status is a noisy indicator of IDGAF. The key point is that IDGAF-positive people who have good jobs still probably don't keep their houses as clean as IDGAF-negative people. So when you control for poverty, you've killed off most of the IDGAF-mediated correlation between lead and IQ, but not all of it.
(as a reminder, this was just a spherical-cow model for illustrative purposes... reality is intractably more complex!)