OK, let's make this clear, because it can be a bit confusing, and anyhow I'm sure Jabba will latch on to it sooner or later:
The statistical math refers to the confidence of the test result. It means that there is a 95% probability that the real age of the fabric is within the stated age range, in this case AD1260 - AD1390. In the remaining 5% possibilities it might be somewhat outside that range, but the odds against it being over a thousand years outside the range are astronomical.
The whole idea of doing such a test, and an absolute prerequisite for reporting such a result is that the sample must be representative. You cannot determine this with mathematics, all you can do is choose the sample location with care.
Thus, the position (but not the size) of the samples is indeed the weakest spot of the C14 test, and if I were to advice Jabba on anything other than to forget about this and get a life, it would be to try to attack the confidence of the samples.
This is, however, also a hopeless task; the sample site was carefully decided on by people with relevant expertice, the sampling was carefully documented, and since it left holes in the shroud, it could easily be re-examined. Furthermore, none of the persons involved had any motivation to not make the samples as representative as possible.
Hans