It helps to look a bit more closely at what Carroll writes in the Skeptics Dictionary:
Of course, the cloth might be 3,000 or 2,000 years old, as Rogers speculates, but the image on the cloth could date from a much later period. No matter what date is correct for either the cloth or the image, the date cannot prove to any degree of reasonable probability that the cloth is the shroud Jesus was wrapped in and that the image is somehow miraculous. To believe that will always be a matter of faith, not scientific proof. (4)
First of all, Rogers did not speculate that it was 3,000 or 2,000 years old. What Rogers argued was that the lack of vanillin in the fabric of the shroud was a serious challenge to the carbon dating. Flax, like the vanilla bean, contains vanillin. Over time, a very long time, it decomposes. How long it takes, depends on temperature. Given a plausible range of average ambient temperatures during the life of the cloth, chemical kinetics demonstrates that the cloth is somewhere between 1,300 and 3,000 years old and not about 700 years old as the carbon dating suggested. Rogers carefully demonstrated that.
Second of all, we need not ascribe miraculous causation to the image, as Carroll suggests, to infer at some level of certainty that it might be the shroud Jesus was wrapped in. There might be, as Rogers and other think, a perfectly natural chemical explanation for the images. The suggestion that the image might be from a much later period is interesting but improbable. This is what Wilson thought. We will address this possibility, but not yet. We have some work to do in understanding the science and the history, none of it very difficult and all of it entertaining, before we tackle this.