Well, this is the exact wording:
While the second bold statement involves striking the Phantom with your sword, why would they mention Zelda inhabiting the Phantoms specifically? If it was more a matter of powering up your sword so you can kill the Phantom, wouldn't it be worded more like...
Thought of this earlier myself.
Keep in mind the absence of Bellum. In this game, the Phantoms are the guardians of the Tower of Spirits, so they're goodguys. Although it is true they're going haywire, that still doesn't involve Bellum unless that's who the Demon King truly is, which I find...