Most of this argument goes back to the original concept of what a DT is.
A DT (in DMC 1) was just a state where Dante would channel the power of the Devil inside the Devil Arm he obtains. In this state, Dante would merel be "covered" in the demon's power, shifting in and out of its form as he attacked.
In DMC 3, this concept was slightly changed so that Dante could have his own DT, but it would change depending on whatever weapon he was holding.
So, is Nero's DT his own power or someone else's? More than likely, it was someone else's and that someone was obviously Vergil. You see, its not that Vergil's soul ended up anywhere, rather Yamato had its own spirit just like any other Devil Arm.
How do I know? Well think about it? DMC 1 is the only game where Dante doesn't have his own DT and is also the only time where he doesn't use Rebellion. So it's safe to assume that Rebellion had its own Devil and the same can be said of Yamato.
As such, Nero's DT is his own, but influenced by the power of Yamato.
I think Nero's DT is chaneled from Yamato which contains some of Vergils power(like Sparda have Sparda's power) because Rebellion was awakaned by Dante's blood. So i believe that Sparda Yamato and Rebellion are some kind of Devil arm but very special.