No, it was not used as a M, J, or L. At least not officially. It might have played during those flavors when the music computer or whatever failed to play a valid song. A good rule of thumb when you find videos like this is that if there's no narration, it's probably just a BTF song playing.
How does that happen? So TWC just grabbed a BTF song if the music programmer didn't play a valid song? That seems unlikely as the song started right when the LF did, so TWC wouldn't have had time to know they needed a song that wasn't usually used as that flavor. Maybe it played as an L and J flavor due to a technical difficulty? When it played as a BTF, it didn't start from the beginning, whereas it did in the video Chazz posted way back in 2007. I also read comments that suggest this song played as an M flavor before a 30 second commercial that would be blocked out in some areas, so that explains it playing as an M without narration, but that doesn't explain why Chazz thought it played as an L and a J flavor. The description suggests he thought it played as an L with narration. Another song I wonder about is "Recollection" by "Gary Brunotte", it's listed on your website as playing as an L flavor besides H, but there's only a video of it playing as an H, did it for real play as an L? And did "Morning In Martinique" for real play as an E?