It just so happens that I am teaching a class on exactly this topic right now. You can get access to the audio, notes and power point at the web site right now for free. Just go and find the articles on Evidence for Jesus. Here is the simple answer. No! This is not a legitimate criticism of the reliability of the New Testament for several reasons.
First of all, these events were NOT recorded way after his death. The Gospel of Mark was written somewhere in the 50s, or perhaps the very early 60s at the latest. This is only twenty-five years after the events. This not a long time. Human memories are still quite vivid after 25 years. A majority of the eye-witnesses to the actual events were still alive when Mark, Matthew and Luke wrote their accounts. Matthew’s account is of an eye-witness, while Mark got his account directly from Peter and Luke was an extremely careful historian. The idea that the eye-witnesses would wholesale invent incidents in the life of Jesus when a fair number of their hearers were eye-witnesses to the same events is difficult to believe unless we can show evidence that there was some sort of conspiracy. Given how controversial the Church was and the fact that many of the witnesses died for their faith, there is good reason to believe that they would not make up events which never happened. Are the gospel accounts actual transcripts of actual conversations? Possibly not. However, can we accept that Jesus was indeed crucified, that he was in fact betrayed by Judas for 30 pieces of silver, that he did claim to be the Way, the Truth and the Life and can we accept that he did in fact raise Lazarus, that he actually had 12 apostles and did indeed deliver a sermon such as the Sermon on the Mount in Matthew 7? Absolutely yes. Given the large community of eye-witnesses to the ministry of Jesus–one which was at least in the many hundreds, but probably more like in the several thousands, there is no way that Mark could have made up events out of his imagination only 25 years after the events. The hundreds who had seen these events for themselves would have corrected any significant errors. If I were to claim now that the San Deigo Chargers won the Superbowl 25 years ago, everything I said would be completely discounted by my peers. Knowledge as basic as how Jesus died and what he taught would NOT change in such a short time, especially in a movement as large and public as the Jesus movement was in the first century.
We have many examples of historians writing a generation or so after the events. For example, Josephus wrote his Jewish Wars and Tacitus wrote his Annals and Suetonius wrote his Lives of the Caesars, all three about 20-50 years after the events. No one doubts the accuracy of the big picture of what they said, although they might question some of the smaller details. Generally, histories are not written until a generation or so after the events. The time frame when the gospels were written fit the normal period when histories are written. The way the New Testament is criticized and doubted is very different from these other documents because of a hyper-bias against the reliability of the New Testament by the skeptics. This hyper skepticism is not warranted by the facts.
As for why the first gospel was not written until the 50s–about twenty to twenty-five years after the event, first of all we do not know that this was the first written account. In fact, most scholars speculate that other accounts were collected before Mark. It is more like this was the first officially accepted account, not the first written account. We know that there was a large oral tradition passed around in the early church. It is a mistake to assume that the events were not written earlier. The precise reason God chose to have the first permanent gospel written almost a generation after Jesus was killed is something I cannot give a definite answer to, but I do know that earlier on, the church relied on eye-witnesses, but as the church spread outside Palestine and into the Greek and Roman world, it became more important to have more “official” documents. It was at this time that we begin to see the gospels composed and passed among the churches. I doubt very much that it had anything to do with poverty because, although the majority in the church were poor, there were prominent men and women in the church, such as Nicodemus and Joseph of Arimathea from the very beginning.