The sister who survived

I don't understand why in the movie they say Adeline died in the fire. In the book it's not so clear, it's even implied that the one who died was Emmeline. I found this very interesting and chose to believe that's what happened. I think it made the story sadder and darker. It would've been a burden for Miss Winter knowing that she saved the wrong one and taking care of her for the rest of their lives.