This was the moment I realized Twelve is the best modern Doctor. Not because his stories are necessarily better, but because Capaldi is able by sheer force of talent to elevate any story he's in and MAKE it better. As much as I love Tennant and Eccleston (Smith is...I'm sure he's a nice person) I doubt either of them could have pulled off something like Heaven Sent, carrying an entire 45 minute story without a single other actor present.
The brunette was right about one thing. The good Doctor does not understand how the Prisoners Dilemma is supposed to work. His bastardization teaches little to nothing about the subject, other than it is hard to predict the outcomes of our actions (a rather odd position for a Time Lord to take, no?).
The whole point of the scene is his trying to break the self-serving reasoning behind the Dilemma and convince them that war, that killing others to improve life for you and yours will only wind up destroying you in the end, that there's no victory for anyone when war happens.
He's rejecting the prisoner's dilemma as an amoral self-serving rationalization.
Yeah, think about it. Both peaceful = both win. One attacks while other is peaceful = attacker wins even more, surrenderer loses. Both attack = both suffer losses but not as much . But this is A. a gross oversimplification of war and B. really frigging incompatible with human psychology, which is way more likely to choose 'attack'. War, being a collection of many individual events, is so complex that he basically gave each side a coin and dared them to toss it.