Martin, I dont think that is an entirely tenable position to have. We dont know that they were written by eyewitnesses, and we dont know that they werent. Most of the hullabaloo is based on the Synoptic problem - the fact that Mathew, Mark, and Luke look as if they have been copied off one another. But it seems to be lost to most people that the fourth Gospel is not only told as an eyewitness account - in a way that the other three do not - but that its author is the only one of the Apostle's to not have been martyred. I beleive he was exiled to the Isle of Patmos until 80 something AD, at which point he died. If you read it, you will even note more than a touch of egotism from St. John, as he refers to the Apostle John not as "john" but as "the disciple Jesus loved". It was also probably from malnutrition and the isolation of being marooned that he wrote his trippy bestseller called "Revelations". Most people dont realize he was the author of that, and Martin, that sentence is the closest you'll ever find me coming to blasphemy, so enjoy it while you can.
Lastly, the Synoptic problem has numerous explanations, none of which seem to invalidate their authenticity. Luke, according to tradition, was not an eyewitness to begin with, so it lays to rest whether this is a new development. He was, according to tradition, a man of letters and a physican who traveled around Israel, Palestine, and Turkey, speaking to eyewitnesses like Mary and the remaining apostles, and I have no doubt, copying other sources. This leaves the unexplained similarities between Mark and Mathew. Into this gap can be fitted the two document hypothesis, which I wont go into, because like most theories, it relies on incomplete facts. It is very possible that these two Gospels were only named after the apostles who formed the original source materials. It is also very possible that Mathew seems to have a very accurate Greek translation of Hebrew, because the Apostle Mathew did indeed write it in his own language and either translated it himself or was translated by a Greek follower. Perhaps they are derived from an account given by Peter to Mathew and a compilation of Christ's sayings (the two source document theory). We'll never know for sure, and since almost all of the theories leave room for reliable source material for the Gospels, it isnt necessarily a problem.