Sorry, I don't believe "psychometric tests" can do that either. At least not at the level that we're talking about: distinguishing an otherwise qualified person from someone who's got some sort of psychopathology.
I don't believe in employment discrimination on the basis of mental illness. After all, John Nash was schizophrenic.
So what your letting in is a subgroup of people who pass, and psychopaths.
In these tests, they know what to say, what to do, to give a certain impression. These tests can't catch them, because they are not honest, and lack integrity(No consistent values, only ones that benefit them).
There are certainly psychopaths who are hopeless at concealing the fact. These are typically the less smart ones, so you wouldn't meet them; they are more likely to be in and out of prison than your office.
There are also psychopaths who are just about perfect at pretending not to be, and have no intention of ever doing otherwise. You can work with one of those for decades, and never notice a thing unless something extreme enough to make 'acting normal' seem a long-term liability happens.
That's the value of these tests (when properly applied): They allow an evaluator to make statistically accurate predictions of specific types of behavior. The key is the two words: statistically and specific. A single composite score will not tell you anything, but the idea that there's a 68% chance that the person you're about to hire is a schizophrenic kleptomaniac should give you pause.