These 8 laboratories shared the same sample collected from a corner of the shroud. The priests handling the shroud would always hold it by its corners. So the explanation is not as weak as it may sound.
The Carbon 14 dating process is not sensitive to pollution from, say, the sweat or sebum on the hands of people handling it. What's more, the sample was vigorously cleaned before analysis.
The article (the one that this thread is about, not the study) addresses exactly this. The author makes the point is C14 dating is widely misunderstood by non-experts who still decide it's within their expertise to find fault with the it.
Did nobody here read the article? The author covered this:
> … to distort the result by 13 centuries the threads employed in the mending would have had to have been more numerous than the threads of the part to be mended
Furthermore, the samples were examined by two textile experts, and later by a lab that looked for trace fabrics that could have affected the radiocarbon dating, and they all confirmed that the sample was the original fabric.
The priests handling the shroud didn't stop handling it in the 14th century. The fire it survived by dousing with water was from the 16th century. There is no reason whatsoever that all 8 laboratories happened to find the same contaminants from the same century.
The article (the one that this thread is about, not the study) addresses exactly this. The author makes the point is C14 dating is widely misunderstood by non-experts who still decide it's within their expertise to find fault with the it.