Why would we not presume that at least some of the differences between the gospels (particularly Mark and Matthew) are not the result of independent oral traditions? What I think is interesting is that, assuming the names of the books (for convenience, and the order of Mark, Matthew, Luke and John) someone came across what we now call Mark and did not merely copy what purported to be an authoritative account. I could easily see that they might alter style and tone, but to add wholly new material? Perhaps someone did not have a full copy, but only copied parts of another copy, then added to it to record elements of a different tradition, like the birth stories. And Luke, presumably having Mark and Matthew, did not simply copy them, but made more changes. One argument would be that the later authors simply made up the additional information, but another would be that they did not consider the initial material to be fully authoritative because it did not cover all of the material that they were familiar with from different traditions. It seems to me unprovable but perfectly reasonable that there would be a core of agreement (since it would all trace back to the teachings of the apostles) and a certain degree of variance (also tracing back to those teachings). The degree of variance would be notable but not necessarily as substantial as for the Arthurian legends because the period was only about 50-70 years. Surely, no one was thinking that the various accounts would ever be collected together as one book and scrutinized for every little detail, agreement or disagreement. I think such matters are where at least a little humility in making assertions is demanded.