I initially wondered why the recap segment used the standard definition version of TOS clips instead of the remastered ones. Then I wondered if we'd get an explanation for the visual differences. Does Pike find that over time, he remembers past events as though they were the 60s pulp sci-fi novels he enjoys reading?
But, reading this thread, I realized the creators were bluntly declaring that yes, TREK looked like this in the 60s and asking that we accept that it's evolved visually since then but is still the same fictional world. Using the HD TOS clips would have undermined their statement and purpose. Characters are now played by different actors. The roles of model builders, set designers, propmakers, visual effects artists, costumers, writers and directors have also been recast.
I kept waiting for a Steven Moffat joke about the visual differences, perhaps saying Talosian mental projection cast a sheen over related memories, but I now see why there wasn't one.