My pet theory (about contamination with woodsmoke or finger grease) doesn't appear to be supported by the scientific papers. It is as you say - the threads that were C14 tested were chemically different from the rest of the shroud - the result of "invisible" mending.
You theory would require that approximately 60% of the material be 16th Century wood soot or finger grease to sufficiently skew the date from 1st Century to 14th.
The actual discovered explanation is that the sample was contaminated: with between 40% and 60% 16th Century threads, depending on which end of the sample the particular tested sub-sample was cut from.
This differing percentage of Medieval to 1st Century material explains the extraordinary spread of the reported ages, 1260 to 1390 +/- 35 years at each end, from what was thought to be a homogenous sample. It should have been a red flag for the testers when the youngest reported age and its degree of confidence did not overlap the oldest reported age and its degree of confidence! If the sample were truly homogenous and an accurate sample of the shroud, the reported ages should have all tested around a mid point and well within the degrees of confidence for all tests.
Harry Gove, the inventor of the C14 test used on the Shroud, when asked "What would be the age of the original material representing ~45% of a sample mixed with ~55% of material with a known provenance of 1535 to give a result of 1350AD when C14 tested?"
His answer, after doing some calculations, was "1st Century +/-100 years."
That percentage is the estimated percentage of one of the C14 Samples sent to the Swiss lab. Examining microphotographs of the other samples, the percentages of new material was estimated to be from 40% to 60% new. material.