The problem here isn't with the main character's moral philosophy, but with his decision theory. He'd be dealing with exactly the same predicament if the mugger were threatening to harm him . The solution is indeed "don't give in to muggers", but it's possible to define this in a workable way. Suppose the mugger can choose between A (don't try to mug Bentham) or forcing Bentham to choose between B (give in) or C (don…
After all, one of the premises here is that the mugger is a deontologist. He doesn't care about outcomes.