Hi Charles,
To your first point, given that level of education is used in this article as a proxy of socioeconomic differences, I would actually expect it to play a meaningful role in differential health-related behavior, and thus in the observed increased risk of cause-specific mortality among less educated (~ less socioeconically advantaged). There's a large body of research demonstrating the effect of SES, education, place of residence, neighborhood factors etc. -- all contributing to the availability of so-called "flexible resources" -- on various health-related behaviors (e.g. vaccination, cancer screening) and disease outcomes (e.g. cancer deaths). And this effect is not just marginal. So, to me authors' conclusion that you cite looks quite compelling.
To your first point, given that level of education is used in this article as a proxy of socioeconomic differences, I would actually expect it to play a meaningful role in differential health-related behavior, and thus in the observed increased risk of cause-specific mortality among less educated (~ less socioeconically advantaged). There's a large body of research demonstrating the effect of SES, education, place of residence, neighborhood factors etc. -- all contributing to the availability of so-called "flexible resources" -- on various health-related behaviors (e.g. vaccination, cancer screening) and disease outcomes (e.g. cancer deaths). And this effect is not just marginal. So, to me authors' conclusion that you cite looks quite compelling.
However, I think that it is fare to be concerned about reverse causation. Authors touch upon that when discussing limitations of their study. They note that since level of education doesn't usually change in the adult life, it is less sensitive to reverse causation than, for example, SES. Also, they note that "quasi-experimental approaches using compulsory schooling reforms have generally supported the claim that at least part of the association between education and mortality is causal (Lleras-Muney, 2005)."