Originally Posted by johnnysaucepn:
“Well, technically, it's the events of The Day of the Doctor, and his modern selves helping to save the Time Lords, that would have changed the circumstances of the Doctor's death. I don't know if rescuing Clara, as such, would have made the difference, he would probably have gone to Trenzalore regardless. Without the Time Lords, he would have died.”
That's not true because the only reason there was a siege at Trenzalore at all was because everyone was afraid that the Time Lords would be breaking back into the Universe by virtue of the Doctor answering their question. So the Time Lords being saved was always part of history and the reason for his grave at Trenzalore.
Something else must have changed in order to have averted that and the most likely theory is that it was Clara. Except, of course, that it was Clara's presence on Gallifrey that persuaded the Doctors that there was another way than blowing the planet up so, if that was already part of history, then so was Clara!
My theory is that Clara was on a loop. First Clara wasn't the impossible girl but was probably still with the Doctor on Gallifrey. She threw herself into the timestream to become the impossible girl but, either wasn't rescued at the end of it or went on to Trenzalore but failed to save the Doctor. Her fragments were Victorian Clara and Asylum Clara explaining why the Doctor encountered these but never remembered seeing any other fragments up to that point.
Meanwhile, one of the fragments (girl in the shop) arranged for the Doctor to meet Bells of St. John Clara earlier than he had originally met her and this Clara, the Clara of season 7, went on and threw herself into the timestream on Trenzalore a second time.
This time the Clara that emerged was suitably different to the previous loop that she was able to avert the Doctor's fate at Trenzalore.
Now there is no grave at Trenzalore and no timestream representing his corpse.
Just a theory, of course, but it works for me