We know of Homer's epics, for example, which are widely availible and popular even in our day and age, but what governing body (if any) at the time 'confirmed' tales such as his as valid mythological pieces. Moreover, are the mythological tales that have survived to this day more akin to novels or more so towards some sort of centralized religious body that laid out what was to be believed and documented for posterity?
This question makes an assumption: That there was an established canon for Greek mythology. There was no Hellenic Pope, no council of Temples to carve out what was canonical in Greek mythology and what wasn't. Contradictions are there in these myths, since these stories come from different places. Aphrodite is considered daughter of Zeus and Dione in the Iliad, but was born of the sea foam a la The Birth of Venus in the Theogony. Both of these pieces were poetry, by the way. They were oral tradition for quite some time, but were recorded as poetry but prose writing was there as well. Some believe that Aphrodite's origins can be traced, in part, to the Mesopotamian Ishtar and many other myths can be traced back to older beliefs.
Proto-Indo-European beliefs were myths of the Proto Indo European peoples and worshipped figures who can be seen to be linked to many myths from many cultures, so some myths may have evolved from these original beliefs. (Take these all with a bit of salt though, we should be careful about assuming we have a deep understanding of the P.I.E. religion) The most notable of these mythological figures is Dyeus Phater, a god of the sky with links to the Roman Jupiter, the Greek Zeus, the Illyrian Dei Patrous, and possibly even the Vedic Dyaus Pita. So myths may have evolved as folklore along with language, slowly growing and changing over time as people moved to new locales and their languages changed as well. I'd figure the Greeks didn't have an equivalent for Ganga, the goddess of the Ganges river, in the same way Hinduism has no Mount Olympus (not to say mountains and rivers were not sacred, just that cultures probably would have adapted to where they migrated. This is a bit of conjecture on my part, so take it with loads of salt).
Myths were above all things that grew and changed with time. For example, Dionysus, the god of wine was believed for a long time to be an import god, since he takes a while to enter the mythos, but research eventually proved he was older than people thought and his origins could be traced back to Mycenean Greece (think ancient Greece for the Ancient Greeks) meaning he is ancient. We think that he was worshipped by a mystery cult which worshipped him and wine before he eventually gained more mainstream popularity. He may have been tied to wine cults who worshipped the state of intoxication brought on by the drink. He may have been worshipped in a different, more chthonic aspect, meaning in a way more related to the dead and the underground. In these earlier myths, he was killed as child and then born again, and this may have been linked to the process of grapes being made into wine, how they are crushed in the winemaking process. He may have been worshipped in secret (hence the phrase mystery cult) which shows that Greek myth didn't really have much centralization. There wasn't some overarching church trying to crack down on heresy. The Romans, however, did go out of their way to try to stick gods together, or syncretize their religion with those of their conquered subjects. We know about cases like Artemis being merged with Diana or Zeus with Jupiter, but this goes beyond that. For example, the Germanic peoples. Thor? Are you sure you don't mean Hercules? Odin? You mean Mercury? This is also why the Romans stumbled with the Christians. A single monotheistic God cannot be syncretized with polytheistic ones, for rather obvious reasons.