I would say that anti-intellectualism is more about people putting faith above reason. An intellectual believes they have the superior mind and can reason about anything. An anti-intellectual believes they have no great intellect and rely on alternative senses to guide them.
Intellectuals as a group don't have a lot of common beliefs, so my comment was referring to the fact that you can (almost) always find something that each one believes on faith.
However, a large fraction of intellectuals do seem to believe that they should be in charge or at least have more control. Do you want to argue that that is "reason" based?
I've previously pointed out that intellectuals (1) will "oversell" their expertise, claiming that fact A implies policy B when it actually doesn't and (2) seem to believe that their expertise in one area implies expertise in other areas.