[jlmorton]

That's not really the point. They attempted to control for demographics, and for dietary covariates like protein, total dietary fat, fiber, and saturated fat. But that is a tiny sliver of the possibly correlated factors.

Did they control for the possibility that 1% milk drinkers learned to drink 1% milk at a young age, and that population happens to live in areas further away from sources of pollution, even in comparison with other households in the same income quintile? Did they control for blood lead levels in childhood?

The point is that we don't know what the covariates are. We have no way to even approach the problem.