I disagree. If the agent has a 95% probability of doing the same thing as me and a 5% chance of defecting, I still cooperate. (With 95% probability, most likely, because you gotta punish defectors.)

Indeed, consider the following game: You give me a program that must either output "give" or "keep". I roll a 20 sided die. On a 20, I play your program against a program that always keeps its token. Otherwise, I play your program against itself. I give you the money that (the first instance of) your program wins. Are you willing to pay me $110 to play? I'd be happy to pay you $110 for this opportunity.

I don't cooperate with myself because P(TheirChoice=Defect)=0, I cooperate with myself because I don't reason as if p is independent from my action.