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A person could still have what are considered to be “good” intentions and do something that does not benefit others. For example, in this old Anime show called MY Hero Academia, there was this villain called Stain who had really good intentions for heroes: he thought that heroes should live up to their potential and do their hero work out of dedication, not just for fame and money, but to enforce those ideals, he would attempt to murder heroes whom he believed did not live up to those ideals.
His intentions would be morally right by current philosophical standards on morality, but he was destroying members of humanity, which is not beneficial to those members. His intentions didn’t actually follow the duality, because although he intended for humanity to be heroic instead of greedy, he still had spite in himself, so part of his intentions were for the benefit of humanity, but the other part was not. They were, in fact, for the detriment of heroes he disliked. He was not COMPLETELY following the benefit-intention duality.
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