Since nobody else will...
Did your friend update the game? You have to connect your PS3 to the net and update/patch the game. If you don't, DLC's may not appear.
Had this myself aswell, so if you haven't already, just give it update and you'll be fine.
As Lymle stated, even after downloading, you have to install it. If you're lost, just do it this way.
Re-download = Install (It will appear under XIII-2) = Update Game
If that doesn't work...