A variety of evidence points to Hurt being the "Doctor" who fought the Time War. In "Name", that Doctor broke the promise of holding the name Doctor. So, he can't be pre-Hartnell. Also, various stories suggest that he's fulfilling Eccleston's role.
The other possibility is that Hurt is the 13th or later Doctor. That's possible but produces a less compelling narrative because it's a Doctor who hasn't happened and doesn't tie into events that we know something about. I guess they could work it in, but it just doesn't feel as strong.
So, he's the "Doctor" who fought the Time War. I wonder what name he took? Or was it only the other Doctor's who decided that he wasn't the Doctor?
Moffat has barely mentioned the Time War or anything from the RTD era (except River Song, whom he created himself) in the three years he's been doing the show. So I'm skeptical of the notion that this new plot twist is related to the Time War.
They did focus somewhat on the Time War book in the TARDIS. I know that wasn't Moffat's story but still, they'd didn't have to include it and Clara's reaction. Foreshadowing I think.
The Other may have initially taken the name Doctor, but had to forsake it and start again in light of what happened at the dawn of time travel. Since we know next to nothing about the dawn of time travel, this is relatively fertile ground for a writer.
The dawn of time travel is more enticing and more mysterious than the Time War. An origin story also ties in better with the idea of celebrating and commemorating the anniversary of "Doctor Who" than an event that chronologically happens toward the middle (relatively speaking).
It would be more of an origin story for the new series, rather than the series as a whole. The Time War is more related to the birth of the new series. I think that's what Moffat is going for because more viewers are familiar with the series from 2005 to present.
(Ed. - don't forget that the multi-quote and edit functions are your friends, helping everyone avoid infractions for spamming. )