Sara may not write her stories down, but she's an author all the same. As our narrator tells us, "the greatest power Sara possessed... was her power of telling stories and of making everything she talked about seem like a story, whether it was one or not" (5.1).
When things are really terrible, she pretends that she's somewhere else to distract herself from the bleak reality of the situation. When she's hungry and stuck in the attic, she pretends she's a prisoner at the Bastille: "If I pretend it's quite different, I can [bear it]," she says, "or if I pretend it is a place in a story." (8.66)
But it's not just Sara's suffering: absolutely every situation can be a story. She says exactly that, insisting that "EVERYTHING'S a story. You are a story—I am a story. Miss Minchin is a story" (9.89). What this means is that Sara understand that people have motivations.
Miss Minchin? Yeah, she's awful. But there's a reason to that. Sara knows that Miss Minchin has a story just like anyone else. She doesn't just see people as caricatures, like the dumb fat girl or the bratty spoiled baby or even the snotty stuck-up mean girl. She sympathizes with people because she knows that they have their own stories.
Know who else sees stories in everything? Writers. You get the sense here that Burnett is patting herself on the back just a teeeeeny bit. Like Sara, Burnett is telling stories that transform the ordinary (a little girl loses her father) into the extraordinary (that father turns out to have left her a fortune in diamond mines). And, since Sara knows that everything's a story, maybe it's not so surprising that her story closes with a fairytale ending.