I assume they meant if you look at roughly the same socioeconomic group that lives 500 miles from refineries as opposed to 500 meters you'll find similar numbers for cancer/other stuff. I'm not on either side of the fence because I don't know, just pointing out what was meant. I'd welcome statistics from either case.
The challenge is that it’s very unlikely that race/socioeconomic factors are causal in and of themselves, the reason why you would adjust for those variables is because they are tightly correlated with other causal factors that aren’t being observed directly, e.g. poorer healthcare availability, poorer access to healthy foods, etc.
Environmental pollution very reasonably can be hypothesized to be a causal mechanism behind cancer rates. Exposure to which is going to be heavily correlated with race and socioeconomics.
I may be misinterpreting OP, but their statement came off as “cancer maps are just maps of where poor non white people live, so it’s not the pollution”, but you can’t just “control” for things that way. Given the fact that environmental pollution is a hazard, there’s a reason why that demographic lives there that makes the exposure to pollution not independent from the demographic characteristics of the population.
Isn't causality transitive though? It sounds like you're saying that low socioeconomic status causes poorer access to healthcare and healthy foods, and that those cause worse health outcomes. Yet you're claiming that low socioeconomic status doesn't cause worse health outcomes. That seems wrong to me.
If causality were transitive the phrase “correlation doesn’t equal causation” wouldn’t exist
Surely that's incorrect. The most obvious scenario is A causes B, B correlates with A, but B does not cause A. Whether causality is transitive is irrelevant.
The quote is typically brought up when there isn’t a direct causal relationship between two variables, not when the causality is reversed. e.g. ice cream sales and drownings. In both cases heat drives behavior, but neither cause each other.
I’d say reverse causality is a very common example, particularly in health and medicine (e.g. illegal drug use and psychiatric disorders).