Let's say I want to measure ability in chess. I give everyone a self report survey: how good are you at chess, 1 to 10? Group A averages a 6, Group B averages a 5. Reproduced across time and regions. Is group a better at chess? We have no idea. All we know is that they report a high average than group b.

Switch to big five: "I feel comfortable around people." Rate the accuracy. Even if group a rates more accurate than group b, what do we really known from this? Comfortable is a relative term. Do group a and b have different perceptions or different experiences?

It's same for Big Five. Self-reported neuroticism correlates with, say, diagnosis of depression. It's not just perception because it correlates with outcomes of interest.

But that's not your example. If your example was self reported depression correlates with clinically diagnosed depression, we now know that people can self-perceive depression the same as clinicians diagnose it.

Your example is self-reported neuroticism corresponds with depression. So what? How are we any closer to knowing if we measured neuroticism? Is there a pre-existing link between neuroticism and depression? How did they measure neuroticism to establish that link?