I wouldn't exactly say that. Much of the author historical information seems to jive with other things I know to be true. If you read to the bottom you'll find a very detailed laundry list of references materials which the author claims to be the basis for his history. Trouble is there are no footnotes to compare against. You don't know where specifically he got his information.
There are some assertions (e.g. 500 million Baptists dying over ...) I would challenge him on. I agree with your assessment that there is never a concrete example of the persecuted people. The "Baptists head on a pole for 30 miles" seems a little incredulous to me even for the Middle Ages. This wasn't 4th century Rome.
My understanding is the author considers all "believers" outside organized Church/church from the conception of the Church to be Baptists (not just Ana-Baptists). This seems to be a rather broad brush treatment. I'm not sure if I'm convinced that all these "loose" Christians represents Baptist beliefs even by the author's definition. That being said it would seem equally incredulous to me to believe that there was a period of time (after the 2nd century) when everyone who called themselves Christian was a member of the existing Church. What would one call them? By the author's VERY LOOSE definition (e.g. believe church and state should be separate, immersion baptism, loose denominational structure) you could almost fit anyone into that category.
Even though some of the information is questionable, the author presents some valid points and his history seems to be about accurate. I wouldn't dismiss the entire history. That being said I noticed he left out the London Baptist Confession of Faith of 1610. I questioned why he didn't go into this important document from the Baptist perspective. It would seem to me the Baptists must have start forming before the time he seems to indicates.
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.