Delta should be ashamed for... what? They should have taken action before the guy lied IYO? The system worked here, and you think it's a shameful incident?
The draconian over-stigmatization of mental illness is what drives people to lie about this stuff, BTW.
Agreed, the whole thing is a lose-lose for pilots. In this case the pilot was a bit of an idiot - simultaneously taking VA payments for the mental health disorder while lying and saying that he does not have a record of mental health disorders. The government is pretty bad at cross-department database lookups (c.f. 9/11) but this one was easy to catch.
Other than that.. if you were a pilot, would you be honest about private mental health issues? When it could mean that your career is temporarily or even permanently derailed? It's easy to be a keyboard jockey hero and say yes, you would, but it's awfully easy to say that when your livelihood is not on the line.
I honestly believe the "four eyes" policy the US already had (and was implemented by the EU post-GermanWings incident) is sufficient to reduce the risk of suicide pilots to an acceptable level without creating this sort of situation for pilots. Most people have enough trouble committing suicide on the ground alone - it's harder to do it in the air, and even harder with the guilt of someone watching and asking what the heck you're doing.