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“These manuscripts were originally written in Koiné, or ‘common’ Greek, and not all of the amateur copyists spoke the language or were even fully literate.”
There is no such thing as “Koine” Greek. According to scholars, the Greek NT is an almost literal word-for-word translation from Hebrew original documents; ergo, the translators tried to preserve what they already considered to be holy—ie, the words of Jesus—without changing them more than they had to. IE, the Greek NT is not bad Greek, but it is more like a literary rubbing from an original.
(”Koine” was an explanation invented by some scholars to try and explain why the Greek of the NT was not “classical” Greek.)
(See, for example, Carmignac, Birth of the Synoptics; and Tresmontant, the Hebrew Christ.)
The NT thus bears within it the evidence of its sources being contemporary with Jesus and the apostles.