Yes. Fairy tales can, because precocious girls who like red and dream about wolves chasing them aren't going to automatically assume they'red Red Riding Hood in Musings. Not any more than someone would imagine themselves to be Eve from the creation story here. Make sense?
In Musings they don't exactly understand what they are. Any finding out would likely happen in the human world, in game. Group plottage will probably get characters closer to figuring out their essences once they're in Seattle.