That is actually one of the best arguments against it being a hoax. A medieval faker of false relics would have created as you suggest, using the Bible as a reference.
Shroudie
My argument against it being a hoax--- If it's an artistic recreation of a phenomenon, there ought to be some evidence of artistry, of artifice. Particularly in medieval times, there should be brush strokes, dye, saturation, anatomical impossibilities---something! The thing is too realistic, for that time or any time.
Reasonable people go with the simplest explanation, and right now, given the data we have, the simplest explanation is that it's the burial shroud of a real, really crucified man, scourged as men were scourged in Roman times, etc. Some of the details, eg the crown of thorns, suggest it was Jesus. Likelier than not, at this point.
The real sticking point for most people is not the carbon dating, which is questionable, but the notion that the relic is too good to be true.
Ah yes, that old trick. My how I forgot it. If the description says "tuxedo" and we find a two piece bikini, we should accesp the bikini because it doesn't fit the description. How thoughtless and stupid of all of us. Tell ya what, since you're that gullible, I have this little car outside that looks very much like a pinto - don't let that fool you. It's really a Lamborghini Countache. I'll sell it to you for a cool mill.. how'd that be. Again, don't be put off by the fact that it looks nothing like a Ghini or any of the literature describing one. That's actually a really good sign it is one.