Fair point. The Time War does kind of seem like an event relating more to the new era of DW than anything from the classic series.
The Fourth Doctor serial "Genesis of the Daleks" could be considered the opening battle of the Last Great Time War. What else would the Daleks consider an attempt to retroactively wipe them from history to be? I bet we could pinpoint other oldWho stories that would fit in the Time War story, so it's not an exclusively nuWho event.
HurtDoctor's quote "Great men are born in fire, it is the privilege of lesser men to light the flame" is a very un-Doctor-y quote, so this incarnation is clearly radically different from his antecedents and successors. Was he just "born" that way, or was he coerced to be