The central point, -- that communities most closely resembling Baptists in theology and outside of communion with Rome existed more or less continuously since the days of the Apostles is not substantiated, as you yourself agree. What is accurate, -- that the councils he mentions took place, Constantine was the Emperor and a convert, John the Baptist had followers, Rome is in Italy -- is also common knowledge, and so is his exposition of Baptist beliefs.
If I wanted to "prove" that Americans descended from Mars and wrote a tract that asserted that but also gave accurate astronomical data on Mars and on the US Constitution and government, then no matter how accurate my astronomy and political history would be, my tract would be worthless because of the central thesis remaining without proof.
Well, you're the one who asked for information on the belief-not me. I can't argue whether it is true or not simply because I have not read through the stacks of books. All I'm doing is trying to look at the material objectively.
I have some doubts and have express them but I don't think you or I have the evidence necessary to totally reject the author's premise. To accurately verify his information we would have to trace every single Christian group and their beliefs throughout the history outside of the Church-an impossible task. I can't even keep my telephone numbers organized. This is like tracing the lost tribe of Israel or Noah's Ark in my mind.