Knowing I use TDT doesn't give someone the ability to make the same computation I do, and so engage TDT.

It is possible to predict the output of a system without emulating the system. We can use the idea 'of emulating their behavior' if it helps as an intuition pump but to assume that it is required is a mistake.

If I meet one of your perfectly rational agents who cooperates on true prisoners dilemma, I'm going to defect. And win.

Why on earth would I cooperate with you? You just told me you were going to defect!

(But I do respect your grappling with the problem. It is NOT trivial. Well, I should say it is trivial but it is hard to get your head around it, particularly with our existing intuitions.)