I'm an agnostic who has no dog in this hunt, but the comments weren't that Peter wasn't the head of the church in Rome, but that he wasn't considered the head of the movement after the death of Jesus.
As an agnostic, but a historian, I'm always open to new scholarship on the historical proofs of religion. I recently read "the Jesus Dynasty" which has some very interesting scholarship. Here are some excerpts found at:
Jesus' successors and legacy:
"Although the followers of Jesus reshaped themselves under the new leadership of James, and eventually returned to Jerusalem, there might well have been a period in which they retreated to Galilee in order to sort things out, and that is just what these gospel traditions appear to reflect. If that was the case then the more idealized account of the Jesus movement in the early chapters of the book of Acts is Luke' s attempt to recast things in a more triumphant way." (p. 238)
"There are two completely separate and distinct 'Christianities' embedded in the New Testament. One is quite familiar and became the version of the Christian faith known to billions over the past two millennia. Its main proponent was the apostle Paul. The other has been largely forgotten and by the turn of the 1st century A.D. had been effectively marginalized and suppressed by the other." (p. 259)
"The Nazarene movement, led by James, Peter, and John, was by any historical definition a Messianic Movement within Judaism. Even the term 'Jewish-Christianity,' though perhaps useful as a description of the original followers of Jesus, is really a misnomer since they never considered themselves anything but faithful Jews. In that sense early Christianity is Jewish." (p. 264)
"I would go so far as to say that the New Testament itself is primarily a literary legacy of the apostle Paul." (p. 270)
"There is no evidence that James worshipped his brother or considered him divine." (p. 280)
"...[W]hat we can know, with some certainty, is that the royal family of Jesus, including the children and grandchildren of his brothers and sisters, were honored by the early Christians well into the 2nd century A.D., while at the same time they were watched and hunted down by the highest levels of the Roman government in Palestine." (p. 290)
Basically, I used to be an agnostic and am not any longer partly because of the shoddy historical assumptions among the skeptics and debunkers, particularly when compared with the primary sources. Too often, there is an assumption almost that *because* it is an old tradition, it *can't* be true--no matter what history says to the contrary.
It is true that James was certainly the head of the Church of Jerusalem...and that a sort of nucleus of Jewish Christians had grown around that see until the city was razed by the Romans and the Jews expelled--around 160ish I think it was. I know of, however, no early source that would exactly support the author's theory of "two Christianities", and in particular one which would oppose the headship of James in Jerusalem to that of Peter in Rome. Certainly Irenaeus, writing around 160-170, ascribed to Peter a role which he does not ascribe to James. Perhaps your author is thinking of the Quartodeciman and similar controversies.
Anyhow, here's Eusebius's account of the martyrdom of James:
Scroll down to chapter 23...the excerpt is too long to include here, but basically Eusebius, writing in the early 300s, has a long quotation from Hegesippus, a writer in the second century, narrating James' martyrdom because he confessed that Jesus was the Christ.
I will do some homework in the primary sources though on the relation of Peter to James and see what I can find.