The Shroud also happen to be involved in a fire around the time that the Carbon test date it, hence the burns marks on some of the folds, and fire of course has no affect on carbon readings...
Mike, I cant swear to it, but I think that cleaning the material of any such contamination is part of the preparatory process in doing Carbon14 datings.
I know that I thought the same thing when I read of the early date since it just did not sync with the other facts known about the shroud at the time.
So, I cant blame you for saying that, but I dont think it is a valid concern.