I'm not familiar with the chemistry involved, but I'll concur with norad45. I have also read that tires need to actually be driven around regularly to re-distribute the chemical preservatives within the rubber. I'm assuming that the preservatives on the surfaces that are exposed to air and sunlight become exhausted and more preservatives need to be "squeezed" to the tire surface through driving.
That brings up another question in my mind. Are spare tires made any differently? Those tires often just sit in the trunk for years and years without ever being used. I personally have never seen anything in any of my vehicle manuals about replacing the spare tire after a certain number of years. Well, the manuals always suggest that you drive fairly slowly for a limited distance on the spare, probably mostly to save wear and tear on the drivetrain due to the smaller size of mini-spare, but I suppose that advice also minimizes the chances you'll have a problem with the rubber in an old spare tire, too.