It would seem if you take the bible literally then the carbon dating is irrelevant. If you accept carbon dating for the shroud, you kinda have to accept carbon dating that shows the earth is much older than 6,000 years.
Or not. Using it to refute the age of an artifact is entirely different from using it to affirm the age of an artifact.
Carbon dating has numerous problems and so does radiometric dating. When an Hawaiian lava flow, known to have occurred in 1801, was tested, twelve times, twelve different results were reached, all varying wildly, none accurate, ranging from 140 million years to nearly 4 billion years, with an average between the twelve of 1.46 billion years. It was less than 200 years old at the time.
Not necessarily -- God or the Devil could've fudged the data in the latter case.
But people don't like to open that can of worms for a whole variety of reasons.
Cheers!
...oh, and Happy Easter.