This reminds me of a sceptical programme that aired a year or two ago in which Tony Robinson was the credulous guy and some scientist was his Scully. They tested a different woo each of the three weeks, although it was often clear that they were going through the motions and they often withheld really obvious stuff until the end of the programme to artificially create a sense of mystery and give the programme a structure.
Anyway one week, I forget exactly what the main theme of the programme as a whole was, but one of the things they did was took some bones which were holy relics from a church in order to have them tested. They were supposed to be the bones of a saint. Turns out that some of them were pig, and some of them were something else that I forget now.
The problem with 'common sense' is that it is 'sense by consensus'.
Normally in forensics you do the 'common sense' thing first; i.e. breadth first; you get all obvious or findable 'starts' or 'leads'.
But here is where forensics often diverges from 'common sense', because most people will then happily talk the 'clues' together in a coherent story.
Or they will focus on the one single 'clue' that matches a prior fitting story.
In forensics you then go into the depth of each item and research it until it has told it's own story.
What you end up with is a lot of 'witness material' that each tells it's own story.
The final story is the one that encompasses all these small stories together and has the least contradictions.
The contradictions can occur because reality has a way of making things look to us as 'clues' or because errors have been made in acquiring the evidence.
Now, there are a lot of examples where it is not as straightforward as I am saying now, but this is the simplified basic methodology.
As for the shroud, that is why I want to follow the 'papertrail'. Because if the ownership can not be proven, then not even the carbon dating would matter (that could be because of errors, conspiracies etc.).
Basically, for the shroud to be anywhere near believable, it would have to hold in any conventional way of handling; procuring, using, storing, transferring to others, etc.
If the carbon dating would date it at 33AD (or it may have been produced earlier, and stored before selling, but not later...) we still have to determine that it was indeed a shroud (sweat, hair samples, skin flakes, dirt... all of these should be findable in one form or other, chemically or physically), then next we would have to determine that Joseph really was the one who brought it to Golgotha (or bought it there) and finally that it was the one that was used to wrap Jesus in.
We can go about that from the date of 'procurement' all the way to the present, saying 'X transferred to Y, then Y to Z' or we can go backwards from the present saying 'Z got it from Y who got it from X'.
But if there is a break in that chain, it has to be verified that the two items that were talked about in both chain segments are one and the same.
*That* is ridiculously hard to do.
