Well, I hadn't read any of the further series details yet at the time; and I simply assumed that the movie makers had a pretty good idea that they'd never get funding to make them all, so they clipped out any extraneous mythology and background bits that they could. They also aged up the kids and ignored some of the really eyerolling obstacles that held the first book together, for example, "oh no, I can't fly because Zeus might hate it!" and "oh no, I can't use a cell phone because it'll draw monsters!" and the whole Hephaestus trap (which while being really dumb does also set up some important Ares stuff in later books). It made for better on-screen entertainment that way.

I just mentally compartmentalized it as a separate-but-parallel universe, like the HP books and movies, or Lord of the Rings; undoubtedly, were the movie-makers to continue, there would be alternate causes and reasons for everything important. Might be fun to sketch out, actually. *ponders*