I’m curious...what does his book claim that is incorrect? I have not read it, nor claim to defend his Catholic views.
I do know that here are many HISTORICAL references to Jesus in the historical record. There was certainly a Tiberius and a Pontius Pilot. Herod was real, as there is historical record, outside the bible, for many off Christ's immediate followers.
That being said. To dispute the written traditions of the Catholic Church, and subsequently most Protestant denominations, with unverifiable speculation would be silly if not offensive to believers.