The great minds can date a scrap of wood a thousand years old but cannot date a few scraps of cloth?
The scientists accurately dated what they were given. They dated a sample that was taken in violation of the protocols that had been agreed on—a sample that now turns out to be a melange of old and newer material, that when accurately dated, reports an average of the ages of the older and newer material which accidentally fell within the range the skeptics expected.
Bad sample in, bad data out.