I don't know what Jabba thinks about the validity of radiocarbon dating or any other modern scientific techniques, but I suspect the main problem is that Jabba's religious beliefs mean he will always prefer to believe what is said on religious sites supporting religious issues such as the Shroud.
He thinks that what is presented on sites like that is just as good as “evidence”, as what any scientists can measure by techniques like C14.
In that sense it seems to boil down to something many of us have met with religious people on forums like this, where they end up arguing about the meaning of the word “evidence”, and as often as not end up claiming that anything that is ever said is actually “evidence”, and that unless science can prove something as an absolute certainty then they think all evidence is equally valid, and hence they conclude that their “evidence” is just as good as any opposing scientific evidence. Better in fact, since as Jabba says, there is much more "evidence" on his shroud sites ... ie everything that is said there in favour of the shroud, that's a huge pile of "evidence" confirming his beliefs.