Can muting music actually mute all the music?

Not sure if this is where I'm supposed to post that but; Most of the time I play with the music muted because I listen to my own music in the background, and that's great, until someone with say the Star Guardian Lux skin decides to spam recall and I'm forced to listen to that same tune that doesn't go at all with my music over and over.

So that also applies for stuff like PROJECT Ashe's or Battlecast Cho's dances... I know (assume?) those count as SFX for the skins but it'd be just great to be able to do without.