Best Original Song – Motion Picture
"Atlas," The Hunger Games: Catching Fire
"Let It Go," Frozen
“Ordinary Love,” Mandela: Long Walk to Freedom
"Please Mr. Kennedy," Inside Llewyn Davis
“Sweeter Than Fiction,” One Chance
The award goes to the songwriter, and Demi did not write the song.
And any and all of the success that the song achieves at any point in time is due to the original version that is featured in the film. Demi's version only matters for radio airplay (and streaming, if she makes a video).