I read this when it came out. I think that a lot of people become depressed as a result of poor physical health (symptoms of many conditions include depression, including underactive thyroid which I am battling right now) and I suppose it's possible that some people with depression have inflammation on the brain but I don't think it's as simple as that. For instance, the article mentions that people with rheumatoid arthritis suffer from depression - that's not surprising as its a very debilitating illness. But people with that disease are treated with anti-inflammatories - which should treat any inflammation on the brain surely?
Depression and other MH illnesses are so complex, and we know so little about the brain, that a sweeping generalisation like this article is difficult for me to believe.