I get what you're trying to say. I know of a few Ph.D's who are complete social dropouts and totally incapable of performing many basic tasks that require intelligence outside of their field of expertise.
We are likely born with an already installed IQ, which can be measured in early childhood. If it happens to be much under 100 then we've been dealt a bad hand and usually won't go on to achieving a higher IQ.
I think we can generalize the expression. yes ,there is no problem to generalize it.
just look at the big picture of worldwide, how many does professors exist? (numerous)
and how many of them are so intelligent to be said that were "genius".
no, it is a very small ratio. (under probably 0.0001% or smaller.(predicted randomly))