Not just claimed eyewitness sources. They are apparent from a straight reading. Eg would they have quoted Jesus as saying, "no-one knows the day or the hour, not even the Son" if he had not actually said it? They are claiming that the Son of God did not know a simple thing like when his return was to be!
The use ion direct quotes, for me, is a clear sign that this isn't accurate. Eye witnesses do not remember detail in that way - they might remember the general gist of what somewhat said, perhaps the basis meaning. But they simply wont remember word for word accurate direct quotes - people aren't some kind of recording machine.
And there are examples whether the 'people in the room' - so to speak have no further involvement in the later events, so how on earth could direct quotes have ever been collected. A couple of good examples are in the nativity story, firstly the shepherds and the angel - no one else was there and the only witnesses (the shepherds) have no further part in the ongoing story of Jesus' later life, yet apparently we have direct quote of the words of the angel.
Secondly the Magi in the presence of Herod - how on earth would direct quotes have arisen and been recorded to be inserted into a gospel some 90 years later. It makes no sense and the only explanation is that the direct quotes were made up for narrative effect.