"You are correct that years after the event it is unlikely that exact words would be remembered."
The point is that believers think that by some means (for example by the inspiration of Holy Spirit) the biblical accounts are accurate.
Of course, the numerous contradictions in scripture don't support the notion that scripture is an accurate account of what was said unless what was originally said was contradictory.
The debates here is with people who believe that scripture is an accurate record of what was said and is not contradictory.
"Does not change that Jesus never said himself he was God (as claimed in the Bible"
Well, we don't know that because, as you point out, given the time that elapsed between the events and their recording we can't tell.
According to what is recorded, Jesus confirmed Thomas to be correct when he (Thomas) called Jesus God.
and
Jesus referred to himself by the same term that God was supposed to have used at the burning bush incident.
No direct statements, but as good as.
The contradictory and ambiguous nature of scripture will mean that the issue cannot be resolved - hence the debates and fighting.
