This may have been stated by others in the episode review thread, but I support the notion that the Hurt Doctor pre-dates the Doctor as we know him. If one buys into the Carmel Masterplan (which I can understand if people don't), the Doctor may have been The Other, who alongside with Rassilon and Omega helped found the Time Lord culture by engineering the black hole that led to the Eye of Harmony.
In that context, Hurt's line that he acted for peace and sanity makes sense and the Doctor's rebuttal that his actions weren't in the name of the Doctor. I think it works because founding the Time Lords eventually drove both Rassilon and Omega mad (unless they were mad already) and who knows who or what else stood in the way of the founding of the Eye of Harmony.
There's a lot of upsides to telling this story, especially on the 50th anniversary — it could be a key element that led the First Doctor to run all those years ago and it addresses some of the gaps that fans have wanted to learn for decades. I must admit some downsides — modern fans may not know or care about the earliest incarnations of the Doctor and it's very easy to get bogged down in the show's mythology.
However, if a show is going to revel in its mythology, a 50th anniversary is perhaps one of the best times to do it and Moffat generally does a pretty decent job of accommodating new and older viewers. Also, the way this "secret" has been foretold makes it sound like it is the key to everything. Sure, it could be Moffat selling a pig in a poke, but it makes a certain kind of sense to subscribe to the idea of the Hurt Doctor being at the founding of Time Lord society and … being the cause of why we're all here after 50 years.
Some of the other theories could work, but Clara says that she's seen all 11 Doctors and I think it's possible she witnessed the eras and acts described by other posters (the Time War and Sixth's encounter with the Valeyard). Of course, she didn't see the Hurt Doctor's face … and she apparently hasn't remembered the name of the Doctor that she learned during her flight to the centre of the Tardis.