That goes into the analysis, but it doesn't end it.
Not so fast. We generally take authenticity as the null hypothesis in history and archaeology and put the burden of proof on claims of fabrication or fraud. People who argue that the shroud is fake have the burden of proof. Now the question of whether this is the burial shroud of Jesus is largely intractable. But the claim that it's a first-century relic consistent with with the Jesus story is tractable.
When you go to a magic show, you're knowingly entering a context in which you know you're being fooled. The fact that you can't figure out how it was done is overshadowed by an a priori understanding that it's fake and that what you are meant to believe has happened really didn't happen that way. Therefore your analogy isn't very apt.
Oh, wait, it is.
We don't hear about the shroud until medieval times, long after any credible claim to provenance will have evaporated. And it emerges in a context of widespread relic-faking. Churches that can sport the best relics attract the most pilgrimage and therefore the most attention and commerce. Faced with the prospect that the authentic, one-true burial shroud of Jesus was silently preserved for 1,300 years and then suddenly appeared, versus the prospect that a fake shroud was produced at a time when everyone was industriously faking relics, it's safe to say these circumstances go a very long way toward satisfying the burden of proof. It's the equivalent of knowingly walking into a magic show.
We have a reliable method of dating that is independently executed by three different laboratories and confirms a date for the shroud that corresponds to when it first appears in the historical record. There is a shaky attempt to unseat that finding by means of questionably validated methods executed by a single arguably biased research team. That's a no-brainer. The inability to come up with falsifiable hypotheses for how it might have been faked is simply not as perplexing as all that. We don't have an encyclopedic understanding of methods and skills that were available.