Also, pets trigger oxytocin release.

A dog usually also "forces" you to exercise moderately by walking it and exercising while depressed is notoriously difficult to follow through on.

I vaguely remember reading a study that found talking to your dog gave the same result as talking to a therapist, (indicating that talking is more important than having someone listen) but I can't find the link at the moment, maybe I misremember.

Owning a dog is not the only option either, I have fairly regularly lent out some of mine to friends and family going through a rough patch with good results.

I suspect it depends on severity and cause though. If the depression is bad enough you may need chemicals just to get you to a level where you can benefit from other treatment.