This meme will not die, and here you can see it blossoming into something even weirder.
There is one (1) case in the literature, back in the early 2000s, where a department rejected a candidate as overqualified based on a cognitive assessment; the rejected applicant took that department to court and lost.
That's it; that's all the evidence.
Against that: most police departments around the country administer written tests with general cognitive components for which there is a floor score and no ceiling (the POST, the NTN, &c). And virtually no departments --- none I'm aware of --- administer IQ tests.
From all this, we've now got "a federally protected right"?