Actually, it does make note of it:

Although the researchers cannot totally rule out the possibility that people with depression may eat a less healthy diet they believe it is unlikely to be the reason for the findings because there was no association with diet and previous diagnosis of depression.

I tend to eat unhealthier when I am feeling down. Of course, when I resolve an issue with a bug that has been given me trouble, I usually celebrate with unhealthy food as well. Many people have habits that are based on unhealthy food as a reward mechanism.

I think they looked more to people who eat processed foods as part of their normal diet and not people who eat processed foods as a reward.

It would be good to know how much processed food within some recurring time frame - say weekly - the people with recurring depression ate.

there's a correlation between depression and food, but there are also correlations between food and socio economic status. So being low income might also be contributing to mental health (which isn't addressed in the article at all; though they do point out that if there are a lot of takeaway joints near by then the problem is exacerbated...might those areas also be lower income?).

I'd need to read the article again but I think the study was done on civil employees. I don't know how broad the pay range is for civil employees nor if the authors sampled the full range.

The thing to keep in mind is that Western science made a dichotomy between the mind and body for religious reasons. In reality, they are completely interrelated. Eating unhealthy food will eventually affect your mind: right now it's just not predictable how or to what extent.

I was interested that income level was not considered as part of the potential correlation effect. Perhaps they imply that education level approximates this, but we do know that income level is relevant because of the higher "at checkout" cost of actual food. One correlation effect would be the higher income advantage in obtaining and regularly consuming fresh foods and what I suspect would be lower depression rates in general among more affluent participants (this is my postulate, not addressed in the study as far as I can tell).

Note: I'm not saying that poor people are all sad and rich people are all happy. My real world experiences run to the contrary in significant ways. I'm just suggesting that amongst these civil servants, there could be an economic feasibility bias that impacts the correlation and would further suggest against causation.

EDIT: corrected poor grammar.