Cieza-
Your OP assumes, as do some christians, that the gospels were written after the lifetime of the witnesses to the actual events. But the evidence tells us that Matthew, Mark, and Luke, as well as Acts, were all completed by 62 A.D.
Here are 2 websites, one which has a translation of The Muratorian Fragment, dated at circa 170 A.D. (this document tells us when the gospels were written). The other gives the arguments from christian scholars for an early dating of the gospels.
www.bible-researcher.com/muratorian.html
The question of how did they so accurately quote Jesus is still valid even if the gospels were written when Jesus was living.