[delluminatus]

A lot of things "correlate with IQ" to varying degrees. Education level, length of sleep, size of vocabulary, etc. I don't understand why the relationships you suggested would be socially unacceptable.

But just because those two things correlate with IQ (which is probably true, so let's just grant them as true even without evidence for the sake of argument), that does not imply that they are sufficiently strongly correlated with each other to be interesting for hiring purposes.

To see my point, consider that being red is correlated with being purple, and being blue is correlated with being purple, but being red is not correlated with being blue. (at least not without evidence).