I actually think of the Damsel as one of the more narrative-savvy Princesses, up with Tower and Prisoner—Tower's the only one to actually come out and say it, but Prisoner clearly knows enough about how things are supposed to work to pull one over on the Narrator (actually, come to think of it, she knows enough about how things work to know she needs to pull one over on the Narrator). And then there's the Damsel.
The Tower says that even though she could break her chains herself, it doesn't make for the "right kind of story." Even though she has so much power over the player by this point, she still needs the story to be fulfilled in the way it's supposed to be. She needs the player to be the one to free her.
It's a bit similar with Damsel, though you could make the argument that it doesn't occur to her that she could leave her chains until you try to free her—Smitten's line about us needing to "present her with her freedom" could be read either way, and he's not necessarily reliable anyway.
But then the Narrator locks you in the basement, and she says, outright, "We're supposed to leave now." There's a way this story is supposed to go, and she understands what it is. And then a couple lines later, you ask her if she can open the door, and she says this:
"I don't know. Do you think I can?"
It's almost as though she's aware on some level that what she can do is determined by your perception of her. If you think she can open the door, she can open it. If not... maybe she can't. Most, if not all (I'm not putting that much stock in my own memory) of the other Princesses don't show any awareness of how dependent they are on perception. But she gets it, somehow.
How dare you leave those in the tags, @golvio.