Note: There are clinical cases of serious depression, but it seems most cases aren't that.
I like to think this also, but is it actually true? Has anyone done that survey?
Sounds like you don't have any real evidence either.
I certainly think this is bidirectional, and it probably has some common-cause issues too (e.g. if your parents are too depressed to earn high incomes, you're getting an economics-genetics double whammy).
More to the point, though, your narrative is about 'medical' depression causing low incomes. Mine is about low incomes causing 'non-medical' depression, so realistically we're talking about different things. I'm sure they overlap, but I'm also confident that there's a difference between depression from "good life, but serotonin imbalance or immune response or whatever" and "lost my job, lost my house, lost a family member".
Most depression screens don't distinguish "depression because depression" from "depression because my life is shitty", and it's not at all clear that anti-depressants are more effective in one case than the other.
So my main observation here is that the high incidence at low income could be about untreated medical issues, but it could also be about a failure to differentiate medical from situational responses.
Research suggests depression is more like blood pressure, varying continuously in the population. There really isn't a clear line between depression-as-illness and other varieties of depression, only an increasing risk of problems as depression increases.
So in one sense, the research does support what you're asking, in that most people who experience depression aren't extremely depressed. But that's sort of tautologically true, in that if you have a normal distribution, most people won't be at the extreme by definition.
It's difficult to approach these things at a deeper level that I think you're getting at, which is "are most people who are depressed not seriously impaired by their depression" or something along those lines. That's harder to answer because it depends on defining "seriously impaired" which depends on sociological trends and so forth and so on.