I am pretty convinced that the Phantom is not an Assist Trophy, almost (almost) convinced enough to avatar bet it.
But I don't avatar bet for anything.
It's just too different from its normal design--every Assist Trophy we have ever been shown, both Brawl and SSB4--has had their design pretty dang faithfully upheld. Waluigi was the most an Assist's design has ever changed (and that was a light denim texture to his overalls). Skull Kid himself is pretty much a direct copy of his MM model with a higher polycount, down to the finest details.
The Phantom differs from the original design in nearly every single detail, from extra patterning to proportions to armor shape and joint design. Absolutely no Assist Trophy has ever been redesigned to such a state--this is the kind of stuff usually reserved for player characters and related bits.
I've said it before and I'll say it again--if the Phantom is an Assist Trophy, it is an absolutely unprecedentedly redesigned one. Disagree with the idea of it being part of Zelda's moveset if you like, but I don't see any way the evidence can be interpreted for it to be seen as an Assist Trophy.