> Suicide is an example. You can't "overdiagnose" suicide unless you outright lie that it happened.
But you can do that. Throughout much of the 20th century (in the United States, at least), the cops might be willing to just call it an accident (he was cleaning his gun) or an unsolved homicide. Ostensibly to spare the family shame or to allow the family to bury them in the cemetery of their choice.
Furthermore, there seem to be factors that cause upswings and downswings in the suicide rate. There were alot more people jumping out of skyscraper windows in 1929 and 1930 than there were in 1925 and 1926, for instance (though we might expect the opportunity to have been roughly the same). Now, that doesn't directly rebut your argument here. But it would mean you'd need to show that if there is an upswing today that it has lasted longer or otherwise been worse than similar ones in the past, or that it doesn't seem to have the same sorts of causes.
If possible, it might actually be better to pick some other measurable event/behavior than suicide. Psychotic breaks, schizo episodes, or voluntary commitment.