I haven't read through the thread, so I don't know what has been said already, but if you took an average, then of course PhD students are going to be smarter than the general population. The average college grad is smarter than the average person from the general population. However, anyone who thinks having a PhD means a person is brilliant is mistaken. I worked in academia for a short while, and I saw and worked with many people who were either PhD students or researchers with PhDs who were, in my opinion, not very smart at all, and this was in a hard science. It actually really turned me off on academia in general. I will say most tenured professors are quite bright as those positions are generally extremely competitive.
Honestly, after working in academia, I think most Americans who earn a PhD are likely not the brightest as there are much, much better routes to take. Foreigners use the PhD as a ticket into America, but for people who are already citizens, it makes much more sense to go to work in industry or education or something. If you don't believe me, here's a comparison:
My old coworker:
38 years old
Brilliant foreign dude with a PhD and 15 years of research experience.
Works 60hrs/week, makes $45k/year, and gets treated like garbage
Me:
27 years old
Bachelor's degrees only. No PhD. No MS.
Work 40-50hrs/week, made over $60k this year, am appreciated for my work. Lots of vacation.
It's kind of a no-brainer.