That's actually the definition of an eyewitness account. Just because Lucus wrote down stuff people told him doesn't make it any less of an eyewitness account of the life of Yahushua.
Using that logic, we'd have to throw out each and every police statement ever written by someone who wasn't the witness themselves. Or any newspaper or magazine article as well.
We could also level the "can't be verified who wrote it" at pretty much the whole of the Tanakh - Isaiah, Jeremiah, Ezekiel, Ezra, Nehemiah, the Torah, Ruth, Judges, 1 & 2 Samuel, 1 & 2 Kings, 1 & 2 Chronicles, The Psalms, Proverbs, Ecclesiastes, the 12 Minor Prophets, etc., etc., all of which contain no verification as to whom actually wrote them down.
Really, this is all such a ridiculous slippery slope that people are going down, I wonder whether people will ever find their way back up
TWTY website and forum Administrator.
Please respect everyone, and try to not get too heated when discussing one's point of view