I'm not so sure about that. However, I'm also unsure about how to properly express my objection. I will try and maybe then we need to accept that we don't have the same information and Aumann's agreement theorem doesn't apply.
Our brain recognizes a pattern and informs us about that in the form of an intuitive understanding of a part of reality. Our language system then slaps a name onto that concept. However the content of the concept is the part that is formed by our intuition, not the name. If different people use different names for the same concept, that is preferable to different people using the same name to refer to different concepts.
We intuitively understand that people ought or ought not to do something and label that concept ethics or morality. If you think you discovered another concept, it should be named differently, or we could take these as the distinction between ethics and morality and agree that I am referring to whatever word we choose to mean what I intended it to mean.
The other side of that is that I may be mistaken about what people think when they talk about utilitarian ethics or morality, in which case we might have stumbled upon the point where we could dissolve a disagreement which is a good thing. In that case I would like to ask: Is it in your opinion relevant to the discussion of what people should or should not do that I consider certain actions as defecting to which I feel a strong inclination to defect in return including hurting or killing these people in order to stop their defecting? If no, then we are talking about different things and don't actually disagree. If yes, then we probably talk about the same thing and I maintain, that my moral intuitions do play a significant role in the argument.
We intuitively understand that people ought or ought not to do something and label that concept ethics or morality.
We intuitively have ideas that people ought or ought not to do something, and some people end their investigation of morality there, without further looking into what people ought to do, but that doesn't mean that ethics is limited to what people intuitively think people ought to do - ethics is what people should actually do, whether it's intuitive or not. For example, it may seem counterintuitive to push an innocent man in front of a troll...
Preface
I have trouble expressing myself in such a way that my ideas come out even remotely like they sound in my head. So please apply the principle of charity and try to read how you think I thought of it.
Tit for Tat
Tit for Tat is usually presented in a game between two players where each chooses to either cooperate or defect. The real world game however differs in two important ways.
First, it's not a two player game. We make choices not only on our single instance of interaction but also on observed interactions between other players. Thus the Advanced Tit For Tat not only defects if the other player defected against itself but also if it could observe the other player defecting against any other player that employs a similar enough algorithm.
Second, there is a middle ground between cooperating and defecting, you could stay neutral. Thus you can harm your opponent, help him or do neither. The question of the best strategy in this real life prisoners dilemma is probably still unanswered. If I see my opponent defecting against some of my peers and cooperating with others, what do I choose?
Agency
The reason why there even is a game is because we can deliberate on our action and can take abstract thoughts into account that do not directly pertain to the current situation, which I think is the distinguishing factor of higher animals from lower. This ability is called agency. In order to be an agent a subject must be able to perceive the situation, have a set of possible actions, model the outcomes of these actions, value the outcomes, and then act accordingly.
We could act in such a way that infringes on these abilities in others. If we limit their ability to perceive or model the situation we call this fraud, if we limit their set of possible actions or their ability to choose between them, we call it coercion, if we infringe on their ability to value an outcome, we call it advertising.
Ethics
I propose that the purpose of our moral or ethical intuitions (I use the two words interchangeably, if there is a distinction please let me know) is to tell us whether some player defected, cooperated or stayed neutral, and to tell us who we should consider as having a close enough decision algorithm to ourselves to 'punish' third players for defecting against them. And I further propose that infringing on someones agency is what we consider as defecting.
Value Ethics
Utilitarians tend to see defecting or cooperating as pertaining to creation or destruction of values. (Edit:) Three things bother me about value ethics:
1. Valuations between different people can't really be compared. If we shut up and multiply, we value the lives of everybody exactly the same no matter how they themselves value their own life. If there are chores to be done and one person claims to "not mind too much" while the other claims to "hate it with a passion" we can't tell if the emotional effect on them is really any different or maybe even the other way round.
2. It makes you torture someone to avoid an insanely huge number of dust specs.
3. It makes you push a fat man to his death.
Agency ethics
Instead I propose that defecting in the real world game is all about infringing on someone's agency. Thus we intuit bankers who destroy an insane amount of wealth while not as good people still as neutral because they do not infringe on agency. At least that is my moral intuition.
So infringing on agency would make you a bad person, while not infringing on agency doesn't make you a good person. What makes you a good person is increasing value. Maybe agency is more fundamental and you cannot be a good person if you are a bad person, but maybe you can be both. That would create cognitive dissonance in people who consider ethics to be a singular thing and don't see the distinction, and that might be at the root of some ethics discussions.
Evil
In my version of ethics it counts as evil to push the fat man or to switch the tracks, as that would mean deliberately causing a death of someone who doesn't want to die. I would let the five die and not feel guilty about it, because I am not the cause of their deaths. I make a fundamental distinction between acting and not acting. If I hadn't been there the five would still die, so how could I be responsible for their deaths? I am aware that this view makes me evil in the eye of utilitarians. But I see less people acting consistent with utilitarianism than I see people arguing that way. Then again, this perception is probably heavily biased.
Conclusion
I don't really have a conclusion except of noticing that there exists a disagreement in fundamental morality and to inform you that there exists at least one person who considers infringing on someone's agency as defecting in a prisoner's dilemma.