@Lightwizard,
Im aware of the erroneous C14 testing because an art student (a fibre artist) made the observation that the sample for C14 was taken from a new weave area(This was "missed" by the STURC group). The fibre artist was ignored and the sample was taken from an area that later was confirmed to be mixed with new and old fibre weaves. (A confirmatory analysis of the weave was done at the Winterthur conservation labs here in nearby Longwood PA)
So, to have the shroud test out at anything pre 1400 meant that it was older and the "brackets" of error need adjusting. The historiographic accounts of the SHroud go back to at least the late 900's as a "holy relic "acquired via the Holy Roman EMpire.
However, with the documented fire in the early 1500's and the use of carbon based solvents in the storage box, as well as wood fumes, I wonder whether there was anyone competent in C14 from the get-go. There was so much contamination from the outset that any C14 would be suspect.
I think that all they can do is to do a series of samplings and and subject them half to cleaning by non solvent means and then leave the other half of the samples uncleaned. Then C14 is run and a statistical sample is presented from all the cleaned v uncleaned samples. This would be the only way to "bracket" a closer determination of the shrouds "Sell by" date in which the samples would confer that the Shroud could not be any younger than but still could be significantly older. There were some decent (supposedly) radioisotope researchers involved and they all screwed up .
Im gonna say that the SHroud is probably from the early Mideaval times, and no amount of scientific testing is gonna bracket it any closer, theres just . been too much junk in the shroud