Jenkins is very credible in that he is not even a Catholic himself.
The show mentioned his other book - something like "the new face of Christianity" or "the coming Christianity" - which also sounded interesting. He says that Christianity (particularly Catholicism) is booming in southern parts of the world and that in 50 years only 1 in 5 Catholics will be white. He also says that "southern" Catholicism is much more orthodox and so this will have profound changes for us here in the USA. Gives me hope although I most likely won't be around to see it (I'll be 94 and in a wheelchair with an oxygen tank trying to light a cigarette).