I think that is a really bad attitude/approach to have. There is great stigma attached to mental illness, and men especially are prone to denying potential mental health problems because of the stigma. I think deep down we all WANT it to be something physical because then we can justify our symptoms. Nobody will blame a person missing a leg for not having the most positive attitude all the time. If it is actually mental, people connect that to being "crazy", "weak", not manly, someone making excuses, etc
I don't think these people are helpless and pointless to spend time on, I think they just need a little clarity, education, and some encouragement, and I'd wager many of them would be willing to face their problems. But I have to say if I had a doctor/psychologist who just wouldn't listen to me if I questioned the results, I'd question how good they were at their job.
Yes, we might be the authority on a diagnosis, and yes the test results may be objective/accurate, but some fight back/some questioning, should be accepted from the patients end.