Another good question.
Burning does not alter the ratios of carbon isotopes... unless they are not uniformly distributed in the carbon and one isotope is more prevalent in the burned area. Since this is generally not the case, carbon isotopes are pretty much mixed homogeneously, unless it can be demonstrated that one area has been irradiated more than the other. All things being equal, the CO and CO2 byproducts of combustion would be composed of carbon isotopes in the same ratio as the original material that was burned. The residue of the original would still have the same ratio.
I am aware of all these things; I just thought you had overstated you general proposition, as quoted in my earlier post. My concerns were with the "all things being equal" and the "original material that was burned."
Since the Shroud fulfills the following conditions: 1) Inhomogeneous in a gross fashion--the image does not cover each and every square inch of the fabric 2) The image is a surface phenomenon, not going completely through the fabric 3) There are portions of the Shroud which have been re-woven with fabric of different ages
it would be easy to construct any number of scenarios where a fire partially burns some portion of the shroud (image and not fabric, OR newer fabric but not old, OR old fabric but not newer, etc.) Such an event could throw off the ratio of Carbon isotopes compared to the original, un-burned Shroud. I was not asserting that smoke from burning, or a merely chemical process, in and of itself, would be likely to significantly change isotope ratios to affect the age--only that the fire might consume and send off as smoke, a portion of the relic as a whole. If you then inadvertently chose a sample for radiocarbon dating from an area thereby affected, without being aware that the sample you had chosen differed in gross composition from the artifact as a whole, you might be led to a wrong conclusion.
The same considerations would apply, even without fire, to choosing a sample of entirely old linen vs. mixed new and old, or to a lesser extent (depending on how samples were taken), to other kinds of tests...
Cheers!