True, but you’re accusing him of fabricating stories! Big difference, there!
Umm… Josephus’ autobiography is an appendix to his Antiquities, which he completed in 93 A.D. Are you really claiming that late of a date for the Gospel of Luke? Scripture scholars tend to date that Gospel at somewhere between 60 and 80 A.D.
You’re talking about John 7:15? The quote is actually “How does this one know [the] writings, having not studied [them]?”
They’re marveling at Jesus’ grasp of the Scriptures, given that he’s not a Scripture scholar… not saying “he’s illiterate!”
(In any case, even if they are talking about literacy, the claim is not that “he does not know letters”, but that he does know how to read; their question is how he knows how to read!)
Edited to add:
Your case for an illiterate Jesus has to account for the claims of Luke 4 – “[Jesus] came to Nazareth, where he had grown up, and went according to his custom into the synagogue on the sabbath day. He stood up to read… [and] he said to them, ‘Today this scripture passage is fulfilled in your hearing.’”
Not only did he stand in order to read (‘ἀναγνῶναι’), but his claim was that they had heard (‘ὠσὶν’, or “in [your] ears”) what he had read to them.
Kinda difficult to refute, short of saying “Luke tells lies.”