No, the C14 test has been falsified in several peer-reviewed scientific and statistical mathematical journal articles which demonstrate the test sampling was flawed from the beginning. The test samples failed the Chi-square statistical test which is a standard C14 test used to demonstrate that the sample is homogenous with the item being sampled. The sub-samples cut from a single master sample cut from the edge of the Shroud failed in comparison with themselves, failing to show they were homogenous with each other! This was a huge red flag that something was contaminating them.
The soot had nothing to do with it, that is cleaned off, but a patch with more modern threads/material invisibly rewoven into original material could skew the dating if there were enough more modern C14 in the newer material to outweigh the older, depleted C14.
Those who dispute the chemically tested findings that alizarin, madder root dyed cotton threads with which had been retted with a more modern method using Alum were found on one side of that area as opposed to un-dyed, older raw, flax based linen on the other, base their disagreement on just claiming those scientists are merely lying, despite the clear evidence presented in their peer-reviewed published papers. Essentially, they wish the evidence away, refusing to see it, claiming it just doesn't exist.
I think, Jenny’s conclusion is not supported by her own text. As she writes:
1. Generally speaking, accurate dating requires more than C-14 alone. [...]
2. C-14 dating is not necessarily more dependable than other methods. In fact, it can be undependable for some very specific reasons. [...]
3. The 1988 Carbon 14 dating of the Shroud has been the subject of extensive discussion because, in the history of C-14 dating, the shroud is unique —a small, one-of-a-kind sample, a contaminated artifact, making accurate dating harder—and the dating was seemingly affected by various procedural and statistical problems. [...]
4. It’s absolutely true that after the findings of 1988, the idea of error in the carbon 14 dating began floating around. Believers were desperate. Multiple theories were put forth. Some were even supported with real science, but none were definitive enough to actually overturn the findings. [...]
The 1988 carbon dating, once seen as proving the shroud was a medieval fake, is now widely thought of as suspect. Even the famous Atheist Richard Dawkins admits it is controversial.[...]
If we wish to be scientific, we must admit we do not yet know, with certainty, how old the cloth is. [...]
The radio-carbon dating of 1988 is not secure, but it is the only piece of authentic data that argues strongly that the shroud is not, itself, authentic.