Sometimes you hear an argument like this against the reliability of the New Testament documents as sources of information about Jesus Christ: These documents contain material gathered from oral traditions, and we all know how unreliable that is. Word got passed around and eventually disfigured, so we can have no assurance that what we find in the gospels is what Jesus actually thought and taught.
This sort of argument betrays radical misunderstandings about the manner in which early Christian oral tradition was transmitted, and it is worth taking a moment to refute. It doesn't take more than a moment to do so, however, because (i) there is no evidence that early Christian oral tradition was transmitted in this anarchic, uncontrolled manner; and (ii) the evidence we do have indicates the exact opposite state of affairs was actually the case.
Consider this brief passage from the Acts of the Apostles:
Meanwhile the church throughout Judea, Galilee, and Samaria had peace and was built up. Living in the fear of the Lord and in the comfort of the Holy Spirit, it increased in numbers. Now as Peter went here and there among all the believers, he came down also to the saints living in Lydda (Acts 9.31-2).
Notice what we find here: Peter, the leader of the apostles who had stayed in Jerusalem after the ascension of Jesus, goes and visits the churches throughout Palestine. This is important for a number of reasons, insofar as it is gives us a way of understanding how the Christian oral tradition was transmitted and preserved. The apostles and leaders of the church went and visited the various Christian bodies throughout different places of the Roman empire. They were thus capable of correcting mistakes, offering further teaching and elaboration on Christian doctrines, refuting false teaching and teachers, etc. Furthermore it is evident that the apostles and disciples of Jesus stayed in regular contact with one another, since many of them were located in Jerusalem and would go to the Temple together for the prayer hours (cf. Acts 3.1). This means that they could confer with one another, refer to each other's understanding for verification and especially in resolving theological difficulties. The example par excellence of this is the Council of Jerusalem, which is related in Acts 15.
We further understand that the apostles and disciples of Jesus were special authorities in the earliest Christian communities. The word of Jesus was accepted on their authority, since they were eyewitnesses of everything that had happened (Acts 10.39). Thus the earliest generation of Christian converts devoted themselves to the apostles' teaching (Acts 2.42). Not just anyone could teach. The apostles, because they were Jesus' disciples during his earthly ministry and because they were with him from the beginning (cf. Acts 1.21-2), were the ones doing the transmitting and teaching of the oral traditions and the teachings about Jesus.
This hierarchy and pecking order was present in Christianity from the beginning. The letter to the Ephesians tells us that this is the order Jesus himself established, since he gave the apostles, the evangelists, the pastors and teachers, and so on (Eph 4.11). Not just anyone was teaching or transmitting tradition, not just anyone took the authority to pass on Christian dogma, but those who had special calling from Jesus Christ and the approval of the apostles. Note that Paul himself goes to the apostles in Jerusalem and seeks their approval and approbation about his evangelizing (Gal 2.1-9). Even Paul himself considered that all his evangelizing and preaching would have been in vain (Gal 2.2) if he did not have the approval of the Jerusalem apostles, especially Peter and James and John. Everything comes back to the apostles as the authoritative body in the church with regards to teaching and tradition, and this because they were with Jesus himself.
So we have adequate evidence that the transmission of Christian oral tradition in the early years before the writing of any of the gospels was not done anarchically, in an uncontrolled manner as the objection considered here assumes. There is no evidence whatsoever that Christian tradition was transmitted in that way, and certainly when I hear that objection, there is never any evidence brought forth for consideration. The consideration of the evidence we do have, however, suggests the exact opposite picture. So this objection is no good.
When we stop and think about it, however, it makes sense that things would have been that way, that is, that there would have been controls and authority structures in the earliest Christian movement. People in the ancient world were not stupid; it is only the illiterati who haven't read much ancient literature that think so, and in so thinking they show their own stupidity and ignorance. The average person would not have accepted groundless tradition about a would-be Christ; but they would have accepted it if it came from persons who were intimately involved with Jesus himself. The followers of Jesus were known in Jerusalem, since they were seen with him after the Triumphal Entry and in the Temple, etc (see the story of Peter's denial of Jesus in Mark 14.66-72; Mt 26.69-75; Luke 22.54-62; John 18.15-18, 25-27). Thus people accepted the authority of the apostles and their teaching because they were with Jesus; others who were not with Jesus were doubted and not received. This is why Paul has to claim both that Jesus appeared to him and taught him the gospel, and also that the apostles in Jerusalem accepted his teaching and evangelistic calling (Gal 1.11-2.10).