I don’t think it is wise for Christians to be defending the legitimacy of the shroud, for reasons similar to this:
If someone’s faith is dependent on the shroud, or even supported by it, I am not at all sure that it is – in fact, I’m pretty sure that it is not – a good idea. If it is definitively demonstrated, if it hasn’t been already, to be inauthentic (to say it gently), then where is their faith? It was not well-founded to begin with, and God wants our hearts, not a faith that’s based on externals. (Note that I said ‘based’, and not that legitimate externals don’t support it.)