No it's not. Twin-based heritability studies show depression risk has about 10% heritability across all cases and 50% heritability among severe cases. There is a genetic component to the disease.
That complexity is mediated by dozens of genes, but each one gene contributes a percentage to that heritability. Single genes can and will be found which link genotype to phenotype. It is just a matter of time and money.
"Heritable" in this context is a term of art. It is a statistic (H squared) that describes the amount of a phenotype that is transmitted from generation to generation. This value broadly describes the amount of a phenotype which can be ascribed to genetics compared to environment without linking it to any known genes or genomic elements. It is a classical technique that was primarily used before we were able to sequence DNA. This is usually figured out by using "twin studies" which are able to quantify inheritance by comparing two individuals with the same genetics.