Out here in Hollywood, I do not think we would make this kind of assumption. No one would be assumed to know Greek religion/mythology unless it happened to be featured in a recent graphic novel. Perhaps if some underage pop star or ingenue called herself "Phoebe the Goddess" on television or the internet only then could one be expected to know this bit of cultural information.
3. How do we know for certain that American films are the best? By that one key attribute by which all American cultural works are judged: the amount of money it generates, possibly adjusted for inflation and exchange rate. That one criteria above all else condenses all the vague and subjective qualities of a creative work into a single, objective index of excellence. And it is the genius of our culture and civilization to recognize this and put all our energies and resources into this one overarching goal: make more money.
4. Greek religion was always presented to me as "mythology" which implied some sort of fictional folk belief. Actually, what we call mythology is a form of deprecation, the Greek's thought of it as religion and were quite devout about it judging from some of the votive deposits that have been found and described in literature. So where you see the term "mythology" applied to the Greeks, just substitute "religion" and you will be much closer to the reality.
Review of the San Francisco Production of Communicating Doors (spoilers!)