I should have mentioned that the tires were bought new in 2004, and the warranty is good for another 20,000 miles, which is why I was so startled. There are no cracks. As far as the definition of “dry rot” goes, that it precisely why I am asking this question on the forum! I take it to mean a kind of disintegration, not in the tread (I don’t think) but on the side walls of the tires. But I am not sure. He could just have been trying to sell me new tires, for all I know.