So, here are some of the arguments for the accuracy of Jesus' sayings (given the considerable passage of time):
(1) Superior memory of the ancients.
(2) Jesus' sayings were actually written down before the gospels.
(3) The disciples had to teach it, so they knew it.
(4) Divine inspiration assures the accuracy.
I think (1) is the only substantial response. If it's true, then it goes along way to helping establish Jesus' sayings as accurate. If there is evidence of (2), I want to know about it. (2) is surely
possible, though. (3) really depends on (1). By itself, I don't think (3) does anything to help the case. For given (possibly) 40 years time, only the short sayings and the parables would likely be very accurate; it's hard to believe the long sermons, which are quite subtle in many ways, could be repeated time and time again without some sort of distortion. Again, if you assume (1) is true, then (3) is much better off. By itself, (4) begs the question, but perhaps a person who has had some sort of religious experience confirming that God exists and Jesus is the ultimate revelation of God could appeal to (4). I don't know; that might be a little far-fetched.
But even if the sayings of Jesus, as we know them, are not entirely accurate, that doesn't mean that God doesn't exist, or that Christianity is false, or that Jesus didn't rise from the dead, or that Jesus isn't the Son of God. None of that follows. I guess what
would follow is that some serious work would need to be done in establishing some sort of criteria to determine which sayings are likely to be accurate and which are not. That might be pretty difficult. But in some instances (e.g., the "palace conversation" between Jesus and Pilate [John 19:8]), I don't think it would be hard to establish the reasonableness of at least a sort of agnosticism about the accuracy of the passage.