Did they have a book where they wrote the stories? They painted these drawings on amphorae, I believe, but i don't think someone from that time would understand these drawings without context.
If it was all just spoken to one another, the myths we know now are probably very different from the original myths the Greek believed?
There's always room for new angles and filling in gaps, but here's an older thread on a similar topic:
Alternate views and follow-up questions are welcome, of course.