Hellenization was absolutely Athenian. If you're prattling on about Byzantines helping spark the Renaissance, then the pathway of Aristotle (an Athenian) -> Alexander the Great should be accepted by you as well.
One is anecdotal. Byzantine refugees brought it to Italy, etc etc. The other is direct and concrete. Aristotle was a tutor and mentor who gave Alexander Athenian ideas on governance, law, philosophy, etc. He then executed them.
There's also two other arguments you're forgetting. One is that we were prohibited from choosing Greece as a civilization by GM. Thus you don't see us talking about Sparta, Thebes, etc.
Second, without the Athenian navy at Salamis, the Achaemenid Persian Empire would have taken over Greece. That is indisputable. After Greece, who else was there to stand in Persia's way? The remaining Greek colonies were weak without an Athenian leader. Carthage and Rome were in their infancy. It is entirely possible that the Mediterranean would have become Persian. Similarly to how it is possible that without the Byzantines, much of Europe might be Islamic. Well, except for the fact that the Franks had already crushed them at Tours.
Tell me, what is of greater impact on the modern world - that Rome ever existed, or that the Balkans remained Christian from 800-1350?