Right. It wasn’t a piece of First Century cloth.
If by that you mean that part of it wasn't First Century cloth, then no, you are wrong because, it was part of a First Century cloth because the 1st Century threads were still part of the original Shroud with newly added Seventeenth Century threads added.
The newer 17th Century threads were added and woven into the original existing 1st Century threads of the Shroud Cloth without removing them from the cloth.
If, you mean it was not a purely 1st Century cloth, but rather a contaminated 1st Century cloth that was tested, then you'd be right.