Those "modern fairy tales where the princess saves herself" types of books not only misrepresent the gender roles in fairy tales (there are tons of stories where girls get to save the day), but they fundamentally misunderstand the entire genre.
Fairy tales aren't about saving yourself.
These aren't epic myths or heroic legends about the great warriors who slay every monster in their path because they're so awesome. Fairy tales are almost always about ordinary, even incompetent, people who get thrown into strange situations where they only succeed because of the help of others.
It's not a gendered thing. The boy who goes off to seek his fortune is usually the dim-witted third son whose older brothers are the strong, smart ones. The third son succeeds because he is kind to the magical helpers who then complete the tasks for him--and the exact same thing happens when a girl is the main character.
The characters in a fairy tale rarely succeed because they embrace their own strength and take their own path. Much more often, they are told step-by-step what to do, and they succeed because they obey--respecting the wisdom of others.
The core virtue of a fairy tale is not pride, but humility. It's not a story about the strong, but those who are weak, small, helpless. The people who can't do it all on their own, but can recognize the worth and wisdom of others.
Turning this story into a "girl power" (or even a "boy power") story warps it into something that is fundamentally the opposite of a fairy tale, and it has nothing to do with the gender of the main character.