I think he means the scene in the warp core which is lifted entirely from TWOK and even recites the same lines but different characters speak them. I was not comfortable with it thats for sure!
But getting back to where this all started, Kirk is promoted from cadet to Captain against all common sense, in ST:09. Then demoted at the start of this film cause he's clearly not ready. But at the end of ST:ID, he was again in command. But in everything I've read, no where do I see he understands and accepts what he did was wrong. He simply gets rewarded for saving the day again.