Good news for you people.
On the EU PSN it seems like Sony/SE made a mistake and instead of the FFVI Music Pack DLC for Dissidia 012, they let you download and activate the Final Fantasy IV Complete Collection!
0.99€ for a game which is labeled as 34.99€ itself.
I tested it, its fully working on 6.37+ OFW, but the license file that comes with activating it is falsely labeled as Dissidia DLC.
However, it is fully playable and runs just fine. Don't get confused that your 3mb DLC wants to download 726mb instead. You'll be happy.
However, I recommend using MediaGo to download your (almost) free game, since downloading that much via the PSP's inbuilt WLAN will be a drag.
(should be possible for most other CFWs as well in one way or another. Use Google!)
Download this version.txt file.
Put it into the "seplugins"-folder on your PSP,
Go to the Recovery Menu and activate "use version.txt in seplugins".
Your PSP should now be disguised as 6.39 and will pass the version check when starting FFIV.