"Back on the Radio" by The Hiss - was this ever in Burnout Paradise's soundtrack?

Back in the day as a kid I would listen to this Burnout Paradise soundtrack YouTube playlist. It had all the songs you'd expect, but for some reason there was an entire video in the playlist for The Hiss's Back on the Radio.

It wasn't a simple lyric/music video for the song, it had the Burnout Paradise cover as if the song was actually in the game and apart of the soundtrack. I always found this interesting as a kid and even would go into the game and carefully search the tracklist to no avail.

I actually found the exact video here: https://www.youtube.com/watch?v=2GA5P4IMQ-8