This isn't true either. Statistical dependence does not determine or uniquely identify causal interpretation or system structure. See Judea Pearl's works (e.g. The Book of Why) for more on this.
People lacking the ability to self-assess is interesting psychologically. People can learn from experience in many other contexts. People can judge their relative position versus other people in many contexts. Why would they be so bad at this particular task? There could be a psychological underpinning.
Even if it turns out we have useless noise-emitting fluff in the place that would produce self-awareness of skill, that would be a psychological cause of a psychological effect. Not the ones that Dunning and Kruger believed they were seeing, but still.
Now, if you asked frogs for a self-assessment of skill, I would expect that data would not show any psychological effects.