The published assay came with the laboratory's own caveat that oils absorbed over centuries of veneration could distort the measured age, and that caveat was never tested. No scholar holds a position on what a clean measurement would show, so this is a gap rather than a disagreement: the work was started, it reached no conclusion, and nobody resumed it.
What would resolve this A repeat assay on material cleaned by a published decontamination protocol, run blind across more than one laboratory, with the sampling location on the cloth recorded. Independent characterisation of the absorbed organic contaminants would show how large a shift they are capable of producing, which is the part the original caveat left unquantified.
OpenRadiocarbon dating and archaeometry, with textile conservation science for the decontamination protocol.Mark Guscin, The Oviedo Cloth