Well, we don't know that we couldn't if we were able to easily take a blood test of the brain. I think there's two parts to the theory, the stricter interpretation that goes something like "depression is just the symptom of too little serotonin - which can be fixed by SSRIs" is quite weak. But the fact that brain chemistry affects mood, and in particular that increasing some chemicals can induce pleasant feelings is pretty robust - we have drugs like cocaine and heroin to thank for that insight. However translating that knowledge into meaningful treatments of depression is not straightforward as the body has a lot automatic control systems trying to keep things in balance.
So at one level we could claim that indeed depression is caused by "too low" serotonin/dopamine levels, as temporarily increasing them will take away the depression, but on the other hand this insight in itself doesn't provide us with a clear path for diagnosis and treatment, and it doesn't preclude that there's other things that's a root cause, such as thought patterns, neurological setup, etc.