Yeah, I know Dylan nor lebeth gave any "official" answer, but I think having to have the same song, .ash file, copyright problems, etc. are reasons enough to consider them a why it hasn't been implemented.
well it seems to me that as long as the file you generate when you record the demo has track, slope, and traffic information already recorded into it, the whole demo wouldn't exactly need the precise mp3 file. so players without the song could still view it (however not listen to the music) which even still would be helpful to some players who want to see how others accomplished certain things. though what could be done as well is have audiosurf also record the song information (bitrate, size, title, etc) and run a comparison to see if the other player has a matching version and allow that one to be played along side it.
this method might make the demos a bit larger than what was originally intended as far as demo recording (as in simply recording the information about player location and running the .ash file and mp3 file with it) but i can see how this would avoid copyright issues.
laser also brings up an excellent point in how even local demo recording would be a huge help to us making demos. fraps effectively limits the fps we can play at (either artificially or because some of us just don't have super computers) and thus gives us hard times with recording / encoding while at the same time giving us a definite disadvantage in our runs. trying to stealth a song with 370 traffic and lots of red zones becomes pretty much exponentially more difficult the lower fps you have. so even though most people wouldn't be able to run my idea of the demo file with music, it wouldnt much matter since it would also make fraps video recording all the easier to upload with music anyways.