Let me very briefly compare the story that I have actually written with mythology, to answer the question. I wrote drama story back in high-school for a class assignment. If we put it under a genre category it may have been under fiction-fantasy mystery. I notice Some Myth relates to a certain belief or religion of a specific society e.g mahabharata is closely associated with Hindu, a religion majorly embraced in India, while my drama story didn't have such characteristics. Another characteristics of myth would be word of mouth story told without any traceable written record like history. In addition, the specific time of when story happened aren't mentioned with some geographical location that no one can exactly point out where on the map while as I can remember My drama story exactly mentioned the where setting took place e.g in a police office. It wouldn't be worldwide popular like Greek Mythology, Indian Mythology, Norse Mythology, if published.
if we could be sure who the author of mythology was, he must have been not the same type as I am, as I am not confident I could write a story as his.
Some Movie director that adopted mythological story may not be confidently creative enough to come up with completely different story line and character as the original one. Or perhaps they are just afraid of some change. Let's take an example. Disney Hercules 1997, most of the story still adopt the original myth. Hercules was adopted as human child, he possess superhuman physical strength and he must accomplish some tasks so that he can go back to Olympus, where he originally hails from. If they created completely a new story than what it was well known for centuries, they might have hardly got market acceptance.
However, Well if business related thing didn't matter, like we created a new myth but only for art class assignment, we did not intend to sell it as a movie, hence not too much worry whether or not the movies is marketable, then, art student whose story teller aptitude might be able to come up with a new story.
But, Percy Jackson the series despite noticeable adoption of greek mythology, are a bit improvisational e.g Zeus' lightning bolt is stolen.
If you addressed the question to me as an individual, then my answer would be I am probably not a mythological story teller. But someone else might be.