Minecraft Playstation 3 Edition loads as the demo unless there's an internet connection. Why?

Any time I load the game while offline (I did indeed buy the full game), it only loads the demo. It will not become the full version until I exit out and connect to the internet. Because I can't always connect easily, this is a problem. What can I do to make it so it loads as the full version when offline?

Because the Demo version is presumably the exact same as the Full version, just without the ability to play online. If you can't connect to the internet, then you can't play online, thus resulting in your game just being the Demo version. Without internet, you're not missing out on anything but multiplayer.