I really doubt it's feasible to memorize it in a single hearing without paraphrasing. The human brain couldn't have been different a few millennia ago, and we know that the greeks used the same memorization techniques we use today (e.g., the memory palace, chunking, ...).

We also see in history specific people tasked with recitation, and high status coming through that ability. Suggesting it's a rare and learned characteristic.

Nitpick: That only suggests that this ability is rare, not that it is learned. (Not saying it is purely talent; everything I know about the brain suggests otherwise. But not just the historical evidence.)