Again, it doesn't matter who's saying it. There's a couple of fundamental console engineering issues here that make that assertion nigh impossible. 1) For DX12 to provide XB1 with a 2x speed increase, its current API must be horrible inefficient and pretty crippled. We know that some of the aspects of DX12 are already present in XB1, so the likelihood of this is virtually nil. 2) Should XB1 become twice as fast, going by multiplat games the hardware will be equal or exceed PS4 in performance, meaning 12 CUs working faster than 18 CUs by way of an API and some ESRAM. Again, chances are basically nil for that happening.
I suppose, playing devil's advocate, Sony's API could be as gimped as XB1's and similarly reducing PS4's hardware to half its performance, and then when DX12 flies in to save the day, XB1 will be unlocked and reaching its full potential which PS4 can't hope to achieve. Realistically though, it's bunk. Consoles have thin APIs (maybe not XB1 with it's 3 flavour Windows base??) that let the hardware run full tilt. People shouldn't be looking for massive speed-ups. Optimisations, sure, but anyone claiming 2x the performance is either being taken out of context (talking about one single aspect being twice as fast), or babbling like a lunatic.