Doesn't this argument boil down to, "Don't hurt the weak because God is watching?"

If your math is telling you this doesn't make sense, remember that math is just a map

Or alternatively, your conclusion might be (not even) wrong.

I agree that there's far more cooperation and far less defection than one would expect if all of human interaction were just true one-shot prisoner's dilemmas; but your explanation for why doesn't ring true to me.

In fact, mentioning "friendly agent C" is kind of begging the question, isn't it? It's presupposing that there already exist powerful cooperators.