I think the problem is a lack of nuance. I think our conscious reasoning tends towards black-and-white predicate logic, but subconsciously, our feelings really do understand the fuzzier Bayesian probability underlying reality.

Thinking that a university degree is 100% certified, stamped proof that someone is intelligent is naive (or perhaps an overly narrow definition of what 'intelligence' is). But so is denying that, all else being equal, a person with a degree is more likely to be more intelligent than someone without until shown otherwise. I don't know by what odds, or by how much, but you must either believe this, or believe that university has no screening or educating effect whatsoever.

Likewise, there are plenty of rich people that inherited wealth, stole wealth, and so on. But for all the others, you either have to conclude that being richer is, at least weakly, correlated with being smarter, or accept that being smarter has no effect on your earning potential. And since earnings are already correlated with value provided to society, you'd have to then conclude that being smart has no value...