This notion of Jabba's that the scientists involved in the carbon dating were conspiring to produce a medieval result makes no sense. Every single one of the scientists involved would be instant household names if the result had been 1st century. They would be world famous celebrities in the same vein as Lord Carnarvon upon discovering Tutankhamun's tomb. This would have been a spectacular discovery that would have rocketed them all to superstardom. They had everything to gain by finding a 1st century date and very little to gain by finding any other date. If anything, the fact that anything but a 1st century result was obtained should indicate that the scientists involved were unbiased and objective to the best of their abilities. Conspiracy theories to the contrary seem like the desperate last attempt of the desperate authenticist to keep their horse in the race (or flogging it as in Jabba's case).
And all this happened with the complicity of the highest authorities of the Roman Catholic Church who have watched a conspiration of rogue scientists wiping out their best evidence of the resurrection of Jesus of Nazareth without trying to prevent this from happening or even telling to the world what was going on?
Who is going to believe that?