The Shroud of Turin has been proven to be a fake time and time again. Mostly due to the material it is made out. The material was not even available in the time period that Jesus lived. If I recall it has been dated between 1200ad and 1400ad.
I'm not a believer but the original carbon dating was from a corner that was cotton patched into the linen so it appears to be invalid.
There is a new request for carbon dating the shroud which may give a more accurate date of the linen.
If this is allowed, and it still shows the age to be less than 2000 years, it wouldn't stop the true believers from believing.
On the other hand if it showed the age to be at least 2000 years, there would be great cheers from the believers.
One thing the believer shows overlook is that the shroud image can and has been reproduced by technics dating back over 700 years.
The history channel show was all about money.