Confused, huh? It’s okay it happens. Let me help you out a little: When Mark says above that the truth claims of Christianity neither rise nor fall on the authenticity of the Shroud of Turin, what he means is "the truth claims of Christianity neither rise nor fall on the authenticity of the Shroud of Turin". He’s a professional writer so sometimes he gets carried away on the flowery verbiage.
Mark Shea says in Shroud of Turin Dated… over at Patheos:
For some, the notion that there is a naturalistic explanation for the Shroud deprives it of a divine origin. Me: I find myself thinking, “Out of all the millions of people who have lived and died, it seems like more than luck that only Jesus of Nazareth should have his image preserved.”
And I can’t help but think that atheists of the gaps sense rather the same connection, since they spend so much time attempting the hopeless task of writing it off as what it obviously is not: a “medieval forgery”.