No. This is one of those tech urban legends that keeps popping up. Facebook does have an opt-in feature that can identify what music, tv show or movie you are listening to or watching, but that's it. http://newsroom.fb.com/news/2014/05/a-new-optional-way-to-sh... https://www.facebook.com/help/iphone-app/369513256545845
That said, this is lazy & irresponsible reporting on what is at best a singlural event.
If it was reproduced, this is clearly a violation of Facebooks terms of service, regardless of if the user has opted to let Facebook listen to the music and TV that's playing in the background.