

We rarely prove something correct. In mathematics, logical proofs are a thing, but in astronomy and physics it is moreso the case that we usually have a model that is accurate enough for our predictions, until we find evidence to the contrary, like here, and have an opportunity to learn and improve.
You really can’t ever prove a lot of things to be correct: you would have to show that no more cases exist that are not covered. But even despite the lack of proven correctness for all cases, these models are useful and provide correct predictions (most of the time), science is constantly on the lookout for cases where the model is wrong or incorrect.
I personally prefer the more complex setup discussed in https://ncase.me/trust/.
The prisoners dilemma is a single decision game: you can tattle or stay silent, and as you don’t know what the other does, and due to how things are set up you would prefer to tattle, even if both staying silent yields better results for both parties.
Politics like this is more of a repeated game, like the one described in the link. You can trust one another, in spite of this single iteration Pareto optimal setting favoring betrayal, and work together. But also; show that you are not an easy mark that can be exploited.