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.
Source? I didn't see anything like that in his authorized biography The Snowball. And it specifically mentioned several times that Buffett always hated manual labor, always ate badly etc.
You're right-the quote showed up in the Google summary of the page, but not the page itself. Weird.
Here is a video where Branson says he achieves "twice as much" on a day when he works out compared to a day when he doesn't exercise: http://www.youtube.com/watch?v=QFjgMKwpz_k
I don't think working out is a necessary condition for success, unless you're so unhealthy as to be physically incapable of doing the things that you need to do in order to be successful.
But the kind self-control you need for fitness could also help you become successful. If so, there might indeed be some correlation between fitness and success.
From personal experience strictly: First and foremost the exercise is something we can all use, successful or not. What working out did help me do is get into a sort of a discipline and made me eat and drink proper healthy food. A side effect of workout, indeed a good one for all us chair-dwellers, is that it fixed my posture as well - no wrist pain, no back pain, no neck pain ...
One of the fittest guys I know, works out and runs several miles every morning, has terrible wrist pain. I know 3 other similar people at my current job.
I don't think your lack of pain has anything to do with your working out. More likely luck, genetics, or lack of other activities that would lead to pain.
Does Mark Zuckerberg work out? How about John Lasseter?
It honestly doesn't seem fitness has any relation what-so-ever to success but I'd be happy to be proven wrong with actual data rather than anecdotes.