OP's own analysis shows that using random data (two variables uniformly distributed over the same range!) for both skill and self-assessment results in a different graph. The original comparison therefor implies another effect on the second dimension, which could be interpreted as: people don't estimate their skills correctly, but drift towards the mean.
But then the question becomes: what did they really ask their subjects? To pick the percentile or a true test score?
OP's own analysis shows that using random data (two variables uniformly distributed over the same range!) for both skill and self-assessment results in a different graph. The original comparison therefor implies another effect on the second dimension, which could be interpreted as: people don't estimate their skills correctly, but drift towards the mean.
But then the question becomes: what did they really ask their subjects? To pick the percentile or a true test score?