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).
http://www.pbs.org/saf/1110/resources/transcript.htm#5
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.