The fact is that the full-disc NXE "install" is not a proper install, in the sense that it does not rely on the game software actually knowing what data was moved on the HDD, or how.
What it does is make an image of the whole disc (like the ISO files, for the less tech-savy) and then mount it to simulate the real DVD. The copy-protection data is treated in a special way on x360 DVDs, and the presence of the DVD in the drive is still required for this image mount to happen.
The good thing is that this way it works for games that had no notion of HDD install.
The bad thing is that those games, like Halo 3, might want to access the HDD on their own and in those cases the performance actually decreases.
If I understood how it works, it also means that no disc swapping is saved by this "installation". The best developers can do is replicate data on several of the DVDs (for example the worldmap in an RPG) so that no disk swapping is needed to access it. But if you are on disc 4, as soon as you access data that only exists on disc 1 you will have to insert it for the copy-protection authentication, even if you had "installed" the actual content.
PS: obviously there's another way: SE could code FFXIII so that it allows an optional real install on the HDD, copying all the data it needs and then only requiring disc 1 to authenticate, a bit like it's done with PC games. But it would be a first, and I suppose that's discouraged by MS.
