Did they have professional historians? What about "pop" history vs "academic" history in their time?
And what do current historians think about their "theories" (if any)?
More can be said, but for one aspect check out: What did ancient historians think of historians? written by u/Celebreth
For modern perspectives, this brief answer: Which ancient historians are most reliable? written by u/Tiako
This answer while not exactly "ancient," this does talk about history in China: Non-Greco-Roman Ancient Historians written by u/Dongzhou3kingdoms