Did you mean to say it the other way around? "Mistaking correlation for causation?" In any case, I don't think they're inaccurately representing the data. They're taking all the data and saying "children who live here are likely to make x% more/less than the national average," which is true. You run the numbers, and that's the result. The correlations are the data.

The article does explicitly discusses this as well, saying: "To remove variation that was simply caused by different types of people living in different areas, Mr. Chetty and Mr. Hendren based the latest estimates on the incomes of more than five million children who moved between areas when they were growing up in the 1980s and 1990s. These estimates are causal: They suggest moving a given child to a new area would in fact cause him or her to do better or worse."

They say that it suggests that this is the case, and discuss what the researchers did to try to isolate cause.