It was explained in various stories, such as "The Day of the Doctor" and "Pyramids of Mars" that the Doctor still remembers the events of negated timelines. He still lived through them, remembers them, and is affected by them.
In "Victory of the Daleks" it is shown that even though Amy has no memory of the events of "The Stolen Earth"/"Journey's End" (they having been erased by the Cracks in Time) the Doctor still remembers them. We also know that the Doctor used up a regeneration in this story. The Doctor explains that as he is a time traveller, and not from the time when the events happened, he will remember these events, because even though they were erased, they still happened to/for him. Thus, even though the events of "The End of Time" were removed from history, they still happened to the Doctor, and he still regenerated.
It is shown that the Doctor's companions will remember events that were erased if they weren't from their own time and space. Thus Amy has no memory of "The Stolen Earth"/"Journey's End", but she can remember the similarly erased "The Time of Angels"/"Flesh and Stone". However "The Big Bang" establishes that all memories are restored after the universe is rebooted (just like a computer doesn't lose its saved data when it's rebooted), so much of this is moot.
There is nothing in any episode to suggest the events of "The End of Time" did not occur exactly as described. In fact the events of the story are referenced in "The Day of the Doctor" by the Time Lord general.