Maybe I missed that part but i don't see how they establish which is the cause and which is the effect. People do switch to healthier or perceiver-to-be-healthier alternatives once they get sick, so it might well be that those with problems switched to vegetable fat. (People in the hospital die more often than those not hospitalised - ergo hospitals kill people!)
And of course the usual link to wider socioeconomic status needs a bit more exploring.
And of course the usual link to wider socioeconomic status needs a bit more exploring.