How do you measure mental health directly? Everything has a sampling bias

Meeting DSM-IV diagnostic criteria

Sure. And how do you determine what percentage of a population fits that DSM-IV criteria?

Great. How do you determine that men and women are seeking treatment at the same rate, and that diagnoses are being given out at the same rates for matching symptoms across genders?

It could just as much be the case that men are diagnosed at a lower rate because they seek out care less often (many studies point at this being true) or that men who do seek care are not diagnosed at as high of a rate despite having the same symptoms (men report higher rates of dissatisfaction with mental care, and other studies show gender bias in diagnosis - men get told to "man up" in so many words-, or men get misdiagnosed because symptoms for the same mental illness vary between men and women)

You might be interested in operationalization. Every measurement is also an operationalization - even things like temperature, speed, and weight.

Eliding or obscuring the act of operationalization leads to reification - treating concepts like real tangible things. I wish reification was taken as seriously as our taboo of anthropomorphization. It happens way more, and sneakily smuggles in human values into the sciences. In some ways it's unavoidable, but being opaque about it and doing it without knowing is a sin.