I liked this argument and I have upvoted your summary below. I will upvote the post as well, if you replace the word "utilitarian" with the phrase "utility maximizer". A utility maximizer is an agent that acts (as though) so as to maximize a utility function, which is what you appear to mean. A utilitarian is a person with an ethical outlook which tells them to maximize the sum of the utility of all persons (with different flavors of utilitarianism using different definitions of "utility", "sum" and "person").