Jabba, the issue isn't whether or not Rodgers is a liar. We have the Vatican itself saying "No, this isn't a patch". We have some of the most well-constrained sampling procedures I've ever heard about. We have video evidence. WE HAVE THE BLOODY SHROUD ITSELF. Whether Rodgers is lying, mistaken, insane, or a purple mongoose that ballances pickles on his nose is irrelevant. Unless you can provide evidence that the sample taken was of a patch--not evidence that Rodgers actually believed what he said, but actual evidence FROM THE ARTIFACT that the artifact itself was not dated--you've got nothing. Period.
There's also the small matter of parsimony. You say that it's unlikely that Rodgers was lying. Okay, fair enough. But if you assume that he's also accurate (as opposed to merely mistaken), you have to assume that 20 Vatican officials with a vested interest in the shroud being a holy rellic ARE lying. You have to assume that the video was faked--because otherwise the video couuld be analyzed and the patch detected. You have to assume that the scientists who dated the shroud were lying--remembering that their entire careers rested on their honesty. (As someone in a similar position, I can tell you that it would have been MUCH better for them to refuse the contract than to do it poorly, and sampling a patch would be the next thing to outright fraud in the minds of, well, pretty much everyone.) A 7 cm piece of cloth is pretty noticeable, so the people who did any repair work, who saw the shroud, or who interacted with it in any way would have to either be too stupid to notice that a patch had been added, or they'd have to be lying. The lab that did the trace chemical analysis on the C14 sample would have to be lying (again, at the risk of their career at best)--or the single greatest fraud in history would have had to have been perpetrated at a time when the technology to know that such things as "water trace chemistry" existed wasn't available.
Simply put, if we assume that Rogers was both honest and factual, we have to assume that everyone else is lying. I realize that it's easier to accuse nameless, faceless mooks of things, but these people are NOT nameless, faceless mooks. They're people with vested interestes in figuring out the answer, in taking high-quality samples, and in some cases in proving that the shroud is from the 1st century AD. Each and every one of them must be lying for your argument to make any sense.
By the way, even if you're right you've got a long uphill slog before you can prove that this is the actual shroud Jesus was burried in. I mean, even if this is 1st century cloth, you have to prove that it was in fact a burial shroud and not, say, some scrap a vendor kept as a display model or something. You have to prove that the image was actually of Jesus (who's actually name was Jeshua bin something), and not some other random person. You have to prove that the shroud was Jesus's burial shroud--tricky business, as provinence for this relic is sketchy at best. You have to prove that the image was put there via some supernatural means--which means that you'll have to demonstrate that the supernatural exists. You'll also have to explain why the shroud doesn't follow the biblical description of the burial (again, the head-cloth wasn't near the body--I sat through enough Easter Sunday masses to remember that).
Every single piece of that--and that's just the beginning, really--needs to be established before we can rationally even tentatively say that this was Jesus's burial shroud. If any single bit of data here is missing, the BEST conclusion we can draw (from the perspective of someone who wants to believe) is "We don't know". And that's true even if this IS Jesus's burial shroud.
All of this is rather rediculous, by the way. The shroud is a facinating historical relic in its own right. Even if it's a Medieval forgery (and it probably is) it's still important historically--someone had forge the thing and for some reason, and the how and why are facinating questions. We don't NEED to assume it's anything more than the data (which you've yet to refute, or even fully acknowledge as far as I can see) say it is.