Zuckerberg did 5000 pushups throughout the course of a week[1], which proves that he's at least moderately fit.
Richard Branson's main piece of productivity advice is "work out"[2].
A strong counterexample would be Warren Buffett, who was once the world's richest man, never worked out, and ate terribly.
Ultimately though it's best to look at the studies other responders to your post cited, which do show some correlation between exercise and mental performance.
Edit: forgot my links
[1]: http://venturebeat.com/2009/10/02/mark-zuckerberg-the-evolut...