It wasn't just a housewife studying pictures of The Shroud of Turin who proposed that claim, it was Swiss textile historian Mechthild Flury-Lemberg who was with a team of experts doing some restoration to it.
And it has not become the accepted date, that theory has been rejected by most other scientists who have studied and dated the Shroud.
Read the whole section entitled "The sample was part of a later repair"
that ends with this
Professor Christopher Ramsey of the Oxford Radiocarbon Accelerator Unit who observed in 2011 that "There are various hypotheses as to why the dates might not be correct, but none of them stack up."
Of course you don't have to believe the scientific communities findings. I am just saying that the scientific community and the custodians of the Turin still accept their own radiocarbon dating findings of 1260-1390 CE, as correct.