Unless you are claiming that all observational science is, in fact, not science, then this idea is intractable.
For example - cosmology. We can observe the universe. We can't create any meaningful controls when we do so, but we can use the observed data to construct models. If those models fit our observations, then they are accepted. If we find a situation in which the model does not correctly describe a system (i.e. it has been falsified), then we can modify it, or discard it entirely.
One can adopt entirely the same process to research the effects of lead. We can observe that, based on available data, a certain phenomenon occurred. We can use other sources of information to compensate for other possible causes. If there is information available which contradicts that conclusion, then we can discard the model. Like other scientific disciplines, there is never 100% certainty about the validity of a model, however if adequate contradicting evidence can be shown, then it will be shown invalid.
The "black swan" is a simplistic view of falsifiability. When presented with this swan, one can respond "Ah, you are correct. This is a swan, and it is black; my model for swan coloration is invalid." One could also legitimately respond "Ah, you are not correct; this swan is white, and has been exposed to dye which has made it appear to be black." That is to say that falsification is never absolute, and all observations are subject to confounding factors.
Real science rarely falls into clean classification of certainty and uncertainty; there are always confounding factors, and the model of lead's effect on crime is not qualitatively different.
Unless you are claiming that all observational science is, in fact, not science, then this idea is intractable.
For example - cosmology. We can observe the universe. We can't create any meaningful controls when we do so, but we can use the observed data to construct models. If those models fit our observations, then they are accepted. If we find a situation in which the model does not correctly describe a system (i.e. it has been falsified), then we can modify it, or discard it entirely.
One can adopt entirely the same process to research the effects of lead. We can observe that, based on available data, a certain phenomenon occurred. We can use other sources of information to compensate for other possible causes. If there is information available which contradicts that conclusion, then we can discard the model. Like other scientific disciplines, there is never 100% certainty about the validity of a model, however if adequate contradicting evidence can be shown, then it will be shown invalid.
The "black swan" is a simplistic view of falsifiability. When presented with this swan, one can respond "Ah, you are correct. This is a swan, and it is black; my model for swan coloration is invalid." One could also legitimately respond "Ah, you are not correct; this swan is white, and has been exposed to dye which has made it appear to be black." That is to say that falsification is never absolute, and all observations are subject to confounding factors.
Real science rarely falls into clean classification of certainty and uncertainty; there are always confounding factors, and the model of lead's effect on crime is not qualitatively different.