As another commenter mentioned, both the Iliad and the Odyssey were passed down via oral tradition. If you want to be "pure", the best way of consuming the stories are to hear them.
Additionally, the stories were always meant to be told, retold, remixed, etc. It is very much in the spirit of the original stories for new bards to add their own spin to it. Don't be turned off by the fact that Jeff doesn't read verbatim a translation of the original texts. He adds a lot of extra context you wouldn't otherwise get from just reading the books (context that every other listener in Ancient Greece would have already had that we don't).
[1] Iliad / Trojan War: https://open.spotify.com/show/7w7RMunEMoAapudklkkVgE [2] Odyssey: https://open.spotify.com/show/5vyJGStvyCNkel5Mqxb4OA