Sure, it sounds intuitive, but it's not talking about simply eating what we think is "healthy." It's talking about a Calorie Restrictive (CR) diet. I saw a segment on Scientific American Frontiers the other day about some doctor --(Walford) who was one of the Biosphere2 guys--that has been doing research on how CR diets (you'll lose about 20% off of your "ideal" weight) helps lab animals live too be much, much longer. We're talking to be about 120 in human years.
Here's the transcript of the show. I think if you poke around you can find the video segments to the entire show (if you have the time, the whole thing is worth viewing).
Seems that the more calories you eat, the more free-radicals you produce. And, unfortunately, the influence of anti-oxidant supplements (anti-oxidents are the body's mechanism for fighting free-radicals) are largely ineffective.