But he...doesn't say they were "factually true". He does seem to refer to certain writing as authoritative. But that's not the same thing. At least, to me, there's a big difference between being true or authoritative and being factual.
Why did Jesus need to come to earth to die for our sins?
The reason why is taught to us in Genesis 1 to 3.
So very relevant, the first mention of Christ is in what God says in Genesis 3 regarding what had happened to what God had made.
Genesis 1 lays the groundwork for the entire purpose of the gospel which is the restoration of all things back to where as God says in Genesis 1 that everything is very good, no evil, no Satan, no death.
Genesis 1
31 Then God saw everything that He had made, and indeed it was very good. So the evening and the morning were the sixth day.
Acts 3:20-21New King James Version (NKJV)
20 and that He may send Jesus Christ, who was preached to you before,
21 whom heaven must receive until the times of restoration of all things, which God has spoken by the mouth of all His holy prophets since the world began.
Matthew 19:27-29New King James Version (NKJV)
27 Then Peter answered and said to Him, “See, we have left all and followed You. Therefore what shall we have?”
28 So Jesus said to them, “Assuredly I say to you, that in the regeneration, when the Son of Man sits on the throne of His glory, you who have followed Me will also sit on twelve thrones, judging the twelve tribes of Israel. 29 And everyone who has left houses or brothers or sisters or father or mother or wife or children or lands, for My name’s sake, shall receive a hundredfold, and inherit eternal life.