On the one hand, of course, the poor and lower middle classes find psychological help in distressed situations hard to afford. Perhaps no profession other than Wall Street law firms has taken Americans to the cleaners as much as psychologists and psychiatrists. One wonders how any of them ever get the help they need; our private health-insurance prejudices certainly don't help anyone much with nonphysical ailments, and I doubt Medicare for all would do very much better with mental health, largely because it would have to limit services very strictly to survive at all.
On the other hand, the non-research hand, most people think the rich are crazier than the poor or middle classes, and there certainly is anecdotal evidence for this.
So while it is interesting to learn that the poor have poorer mental health than the rich, I am not ready to deny that modest stations in life might in fact be somewhat healthier, all things considered. You may take my comments as a KNOW-NOTHING sort of reaction to the research presented here -- but not certainly a totally wrong reaction, in my opinion.