The proper question, when faced with 20 bits of evidence that say one thing and 1 that says something else, is "why do these not match up?" And then proper scrutiny should have been applied to all of the evidence but *especially* the anomalous C-14 to see if something went wrong.
I recall a few years ago, an intriguing contradiction was discovered by cosmologists that suggested that the stars within the universe were older than the universe itself. That discovery was not touted as invalidating modern cosmology--it was just accepted as a strange and curious contradiction which further inquiry hopefully could resolve. That is exactly the attitude that should have been applied to the shroud by skeptics.
But many were hell-bent on proving the thing wrong and it blinded them.
Uh huh.