Yes, this is certainly not anything approaching the consensus of "serious historians", this sounds like a crank theory put out likely by a single individual who is publishing popular books on the subject.
The Pauline epistles are indeed though usually cited as the works in the New Testament that were the earliest written down, but there's plenty of reason to doubt the academic consensus, which has shifted over time, and like all historical subjects, somewhat subject to fads. (After all, you can't gain notoriety or publish a new paper that simply says "yeah, what's written is likely true, or the closest approximation to the truth we're likely to ever have, and the people who came before me were right.)
Take the Gospel of Mark, usually cited as the earliest gospel. One of the strongest held reasons that it's believed to have been written after 70 AD is because Jesus prophesies what sounds like the Siege of Jerusalem. That's it. It certainly doesn't seem crazy even from a one hundred percent secular worldview that Jesus correctly or even accidentally predicted the destruction of Jerusalem by the Romans via one hundred percent natural means, given the contemporary political situation. If anything, you can understand how the 1 of 100 prophets who completely by chance made an accurate prediction would become more popular afterward.
Or consider the gospel of John - one of the strongest held arguments against Johannine authorship is about the only biographical information we know about him is that he's a fisherman, and the author of John sounds like an intelligent Greek writer. That's it. I don't think it's radically implausible that he may have been employed at the time as a fisherman, and still had an educated background. Scholars usually call it "anonymous", even though the author clearly focuses on John and refers to him in a special way..and the ends the book by claiming that this is the disciple which testifies these things, and wrote these things. He also repeatedly humblebrags that John beat Peter in race...the kind of detail that doesn't seem like a religious community would find worth highlighting.
It's also not surprising that different accounts of something that occurred over a long timespan contain differences or highlight different things. You see this all the time from eyewitnesses today and throughout history. I was just reading the Landmark Edition of Anabasis that just came out, and there's a whole appendix about how Xenophon and Cyrus's doctor narrate a battle differently and make different claims about how Cyrus was wounded. But they were both eyewitnesses, or the closest to it you could ever hope to get for an event that happened 2500 years ago.