As you mention, most SSRI ads specifically note that it is thought to work by inhibiting serotonin reuptake...maybe. There isn't even strong proof that serotonin plays the part popularly believed.
But SSRIs work for many people, and do seem to have an effect, so the theoretical is good enough for now.
But SSRIs work for many people, and do seem to have an effect, so the theoretical is good enough for now.