My wording is wrong, because it sounds like I'm saying that Bentham is adopting the policy ad hoc. A better way to state this is that Bentham starts out as an agent that does not give into brinksmanship type games, because a world where brinksmanship type games exist is a substantially worse world than ones where they don't (because net-negative situations will end up happening, it takes effort to set up brinksmanship and good actions do not benefit more from brinksmanship). It's different because by adopting C, Bentham prevents the mugger from mugging, which is a better world than one where the mugger goes on mugging. I don't see any contradiction in utilitarianism here.
If the world where the thought experiment is not true and "mugging" is net positive, calling it mugging then is disingenuous, that's just more optimally allocating resources and is more equivalent to the conversation "hi bentham i have a cool plan for 10 dollars let me tell you what it is" "okay i have heard your plan and i think it's a good idea here's 10 bucks"
Except that you are putting the words "mugging" and implying violence so that people view the interaction as more absurd than it actually is.