Ah yes, that classic fansong. Funnily enough, it's actually the other way around, where the fanfic was based on the song.
Also, indeed, doesn't matter where a song originates from, a good song is still a good song.
Take me for example. Just because I lost all love I used to have for RWBY doesn't stop me from continuing to enjoy the soundtrack.

Not too uncommon, really. A lot of great music was made by bronies inspired by the show, sometimes the lyrics give it away, and others you could have someone listen to it and have no idea of its origins.

Same with FNaF. I hardly care about the series, but I've found and loved a ton of songs based on the series that people have made over the years.