One little problem: The Shroud survived two separate fires, which could have affected the amount of carbon isotopes in the cloth. Thus any radiocarbon testing at all, no matter the result, is questionable at best. The issue is explained as part of a discussion here.
The soot theory has also been shot down conclusively.
First of all, there is no known mechanism for carbon-14 to be added to an existing carbon isotope matrix of carbon-14, Carbon-13, and Carbon-12 by chemical means, which is what a fire is.
Since very little of the shroud was actually carbonized by either of the fires, that point is actually moot, anyway.
Exposure to radiation might be able to convert the far more plentiful Carbon 12 into 13 or 14... but there is no evidence that exposure to a fire, even one hot enough to melt silver, would provide any radioactivity.
Assuming that soot from a newly made (from wood grown in the few years before the 1532AD fire), burning casket or church surrounding the Shroud permeated the shroud, the amount of carbon soot required to skew the C-14 date from the 1st century to 14th would be approximately 50% by weight of the tested sample. Again, the soot simply is not there.
(The amount to skew the date is less than the bioplastic residue theory because the wood would have been grown and harvested in a much shorter time period [say 50 to 100 years] than the 1945 years that the bacterial theory would require.)