It’s never easy predicting how Best Song will go. The rule:
An original song consists of words and music, both of which are original and written specifically for the motion picture. There must be a clearly audible, intelligible, substantive rendition (not necessarily visually presented) of both lyric and melody, used in the body of the motion picture or as the first music cue in the end credits.
The tricky part here, Agent Starling, is the “used in the body of the motion picture” part. I am not sure why certain songs are deemed ineligible but every year there seems to be a curfuffle. At any rate, I’m sure Neil Finn’s Hobbit song will be in accordance with these rules. Neil Finn of Crowded House fame. Listen to it here.