To play devil's advocate: what if top CEO's (whether by school or by track record) look for harder challenges?
Someone once said Dara Khosrowshahi took the CEO job of Uber not to make money, but because anyone willing to take that job is somehow who wants to play the CEO game on "hard mode".
If everyone's taking a job where there's a 50% chance of failure for their personal skill level -- which means the more skilled CEO's are taking the harder jobs, and the less skilled CEO's are taking the "safer" harder-to-mess-up jobs -- then statistics will look like CEO skills don't make a difference... even though they do.
And since employment markets (in general) tend to funnel higher performers to harder jobs (because that's economically efficient), this doesn't seem implausible.