In the late 80’s, Andrew Cartmel developed a plan to reveal The Doctor’s origins.  Only a few bits and pieces of this made it to screen- Sevens “I’m more than just another Time Lord” is likely part of this.

Among other things, this involved revising the story of how the Gallifreyans became the Time Lords.  Originally, it was Rassilon and Omega, Rassilon being more on the political end, Omega being the engineer.  He would have added a third figure, called “The Other”, and at least heavily implied that The Doctor is a future incarnation of this figure.  In some of the novels, Susan Foreman was actually The Other’s granddaughter, and recognized The Doctor as a distant reincarnation of her grandfather.

Eleven talking about how Hurt’s character broke the promise does seem to suggest Hurt is somewhere in advance of the first incarnation, but I’m not convinced it rules this out entirely.  Perhaps he adopted the name “The Doctor” in part as a response to his first incarnations betrayal of what he stood for?  He presumably stood for something even before he adopted the name.  Maybe what Hurt’s character did was part of why he left Gallifrey in the first place?