The proverb you mention is overly general to the point of being largely false (or at least unfalsifiable, to give some credit to the defensibility of philosophical solipsism otherwise). @JunJun and @felino's answers also generalize too much, but this is partly a consequence of a lack of specificity in the OP. Depression in general is widely misunderstood and commonly oversimplified.
I prefer to conceptualize depression in general as a latent, dimensional, symptomatic state that is linked to its causes by theory, not by definition. This means not directly measured, not truly dichotomous (like clinical diagnosis often is – people are generally either diagnosed as having a mood disorder or not having one, but whether they truly are depressed is more a matter of degree), not a disease or disorder per se but rather a consequence thereof, and not defined as resulting from any one cause. This concept permits research to identify several partial influences that may operate together or separately to produce depression, and this is in fact what research on depression has done.
As @what points out, depression is known to have both genetic and environmental influences. Environmental influences are certainly not decided exclusively in the mind – this is the first reason your proverb overgeneralizes. Second, genetic influences are hardly decided in the sense of being voluntary. What remains may permit voluntary intervention, but not every case of depression leaves anything remaining.
- Some cases arise entirely due to overwhelming, unforeseeable, and effectively unavoidable stress.
- Some cases arise entirely due to genetic or other neurochemical influences (e.g., drugs, disorders).
Attitude change may aid coping in these circumstances, but one could hardly expect it to cure depressed affect altogether when one has good reasons to feel depressed or no real control over its sources.
However, many cases may arise from problematic attitudes (e.g., low self-esteem, external locus of control, social alienation). As mentioned in my answer to "https://cogsci.stackexchange.com/q/5803/4086" Lyubomirsky (2008) argues that for average people in average circumstances, roughly 2/5 of one's happiness may be altered voluntarily, as through attitude change:
(source: edbatista.com) (Based on Lyubomirsky, 2008)
Again, this won't be true in every case, especially those affected by special circumstances or involuntary or biological factors. Still, in many cases, it's enough malleability to facilitate important changes. In a falsely dichotomous model of depression, it's plenty of room in which to cross a clinical threshold and thereby become "not depressed". From a more dimensional standpoint, it's not going to allow anyone to change from the most depressed person to the happiest or vice versa: it's only enough to allow a percentile change of roughly 40% on average.
Several therapeutic modalities and positive psychological interventions incorporate attitude change, e.g.:
Lyubomirsky, S. (2008). The how of happiness: A scientific approach to getting the life you want. Penguin.