What no one seems to ever bring up is that there has been, for far longer than the middle ages, references to a cloth, in some cases called the "Mandylion" with an image of Christ. Tradition tells us that this is the same one and documents refer to the Knights Templar having kept it for a time. The provenance goes back much farther than the carbon dating. And then the chief carbon dater came to the conclusion that the dating was erroneous.
I'm sticking with the "rich, hoary, decrepit men-on-robes club" (who, incidentally, took a vow of poverty. Material Church "wealth" is in assets held in trust for the inspiration of the faithful) on this one.
“carbon dating was debunked by the very researchers who conducted the tests.”
Quote, link, source?