There are several things we've known since Doctor Who made its triumphant return in 2005. We know that the Ninth Doctor is traumatised, haunted by what he did to end the Time War. He caused the catastrophe that wiped out Time Lords and Daleks alike:
'They all burned...I saw it happen. I made it happen.'
We also know that Rose was a big part of helping him rediscover his better nature and believe in himself again.
The events of the Time War have never been shown on screen. They've only ever been referred to in grandiose terms that suggest they CANNOT be shown, because they're too mind-wrangling: Davros flying into the jaws of the Nightmare Child, the Could-Have-Been King with his army of Meanwhiles and Never-Weres, and so on.
Now, given that the Christopher Eccleston Doctor seems to be freshly regenerated at the start of 'Rose', fans have tended to assume that he looked like Paul McGann, the Eighth Doctor, while he was committing the terrible deed of wiping out his people and the Daleks all at once. It's a natural assumption.
But we've never seen the McGann Doctor regenerate into the Eccleston Doctor. And that's the gap into which the John Hurt character fits. This is the Doctor's secret; while he was massacring the Daleks and his own people, he had John Hurt's face. And for all that he justifies his deeds - 'What I did, I did without choice, in the name of peace and sanity' - he is still anathema, the skeleton in the Doctor's closet. He is the black sheep in a family of one.
So is John Hurt playing the 'real' Ninth Doctor? No. He's playing the ninth incarnation of the Time Lord known as the Doctor, but he doesn't get to call himself the Doctor, because his actions make him unworthy of that title in the eyes of his other incarnations.
Let's say, for the sake of argument, that the Doctor's real name is Ernie Witherspoon, which it isn't, but it'll do. Ernie Witherspoon runs away from Gallifrey in a stolen TARDIS. He adopts 'The Doctor' as his assumed identity; it's a mission statement, an ideal to live up to, 'a promise that you make'. All of Ernie Witherspoon's incarnations except one have lived up to that mission statement. John Hurt is still Ernie Witherspoon, but he's no Doctor.
The source of the confusion is the rather silly title that popped up. 'Introducing John Hurt as The Doctor'. This is the BBC confirming that yes, the John Hurt incarnation is playing the same character as Matt Smith and David Tennant and so on. But he's not The Doctor, because he has no right to call himself that. Not after what he did.
So how do we know John Hurt is playing the incarnation between McGann and Eccleston? Well, because it's been leaked, for one thing. But we also know because Clara found a huge book on the History of the Time War. Now, the Time War only has one survivor, so the book - if it's a complete history - can only have one possible author.
Clara finds a reference to Ernie Witherspoon in the book. The only reason the Doctor would use his real name instead of his proud title of Doctor is if he was talking about the version of himself who defaulted to being Ernie Witherspoon because he had no right to use the title. In other words, the version played by John Hurt.
It's a very clever twist for Moffat to throw in, because it doesn't actually retcon anything. We've always known that the Doctor is ashamed of what he did during the Time War. But we haven't known that all those shameful actions were committed by a hitherto unseen incarnation.
And from a certain point of view, it makes Eccleston's Doctor all the more profound. Because he wasn't just recovering from the Time War, he was deciding to be the Doctor again. The Eccleston incarnation was a chance to resume that title and the moral stance that goes with it, and you can clearly see in episodes like 'Dalek' how horrified he might be that he can't live up to it.
In the end, Eccleston's Doctor proves himself worthy of the title. Faced with the terrible dilemma of wiping out the Daleks and the population of Earth along with them, or taking no action, he chooses to do nothing:
'WHAT ARE YOU, DOCTOR? COWARD OR KILLER?'
'Coward, any day.'
Hurt would have chosen the path of the killer. And that's why the other incarnations deny him the 'Doctor' identity.