The scientist went back to the pictures of the samples, and realized that the couple was right, and that the Carbon 14 dating was likely incorrect, because it was picking up the readings off the newer threads. He thought that new testing should be done, but he died of cancer before anything could occur.
There are samples of the Shroud, from an area that was not part of the re-weaving, though, that could be Carbon dated.
I remember reading something about that situation quite a while back, as well.
In the program that I saw recently, they mentioned the C-14 dating dilemma, also. They talked about how humans handling the Shroud during the Middle Ages had contaminated it.