My understanding, and mind you I don't have a very good understanding, is that generally the network pays blanket music rights, which the skating broadcasts are covered under. My guess is the Animal Channel hasn't done that, partly b/c they don't usually need to, and probably weren't willing to pay the music rights fees to do the broadcast.
CBC often either doesn't get the rights or isn't willing to pay them, so their pro skating broadcasts, at least, often have some cheesy muzak-ed version of the music instead of the actual song the skater used in the show.