The problem is that your argument, even if it is true for a significant portion of people diagnosed with mental illness (which I personally am not convinced of, but also have no hard numbers on hand), makes it more difficult for those people who currently are afraid of how society will react if they attempt to treat their illness. It creates a bar that someone has to be "this sick to get diagnosed". It creates a fear of being told that your problems aren't really problems, and you're just not dealing with them correctly (regardless of the intent of your original argument).
I think that it's not appropriate _right now_ to deal with over-diagnosis as a serious issue in comparison to under-treatment. Maybe, in a future when it's socially acceptable to get help for mental illness, we can deal with over-diagnosis if it's a serious issue. But trying to stamp out over-diagnosis right now contributes to a more dangerous stigma.