It doesn’t make any sense if you wanted to carbon-date the Shroud, no.
But that’s what they did.
They carbon-dated a patch left from a (IIRC) 14th Century fire - a fire that also suffused the rest of the Shroud with 14th Century carbon smoke.
No, it is impossible for that to have skewed the date enough. For that 14th Century fire to have skewed the date to a 14th Century date, the amount of 14th Century carbon added would be almost 100% of the carbon 14 in the Shroud. That would make the Shroud black with soot. IT is not present. We KNOW what skewed the date. They tested a 16th Century patch, mixed with 1st Century original material. The combined melange of materials resulted in a spurious 14th century dating.
Similarly, the bacterial pooping theory fails for the same reasons plus the fact that if the bacteria were eating the material of the Shroud, the carbon they ate and then pooped, would contain the C14 extant in the Shroud, not new C14. . . And would not skew it at all. Only new growth plants can fix atmospheric C14.