If that were true, psychotherapy (especially psychotherapy focused on the patient's relationships) would always work. (Incidentally, at least on the authors is a psychiatrist in private practice, who would want to believe that.) That isn't the case.
I think the rank theory of depression, while similarly characterized by evolutionary/speculative reasoning, makes a lot more sense.
Could it somehow be both? Maybe if you have lower status, solving complex problems becomes relatively more important, because you have less alternative opportunities. For higher-status people, even when they are capable of solving problems, letting other people solve problems and just taking their stuff is probably more profitable. Losing status could imply that you should switch to problem-solving mode, because that's the way to be useful to your new masters (and your quality of life now depends on their opinions).
Since there are intelligent people here who follow the topic of evolutionary psychology, I'd like to hear opinions about some research from 2009. Particularly if this idea seems reasonable or not, but possibly other opinions that people might have about it.
The idea is a variation on one that's somewhat popular here: that some conditions usually regarded as mental illnesses (Asperger's for example) are beneficial, even adaptive. But the condition in question now is depression. Briefly, the argument is that depression, at least when it is a response to stimuli and not a permanent feature, can have the useful effect of encouraging more rational thought when this is particularly important, even at the cost of quality of life, and that this is adaptive.
Links: a Scientific American article, a journal article (which I haven't read, behind a $12 paywall). Here's the abstract of the journal article:
The full journal citation is Andrews, Paul W., and Thomson Jr., J. Anderson; July 2009; Psychological Review 116 (3), 620–654; doi 10.1037/a0016242.