It's consequentialist reasoning, not necessarily utilitarian. And you don't have to be a thoroughgoing consequentialist to agree that in a world full of preventable misery, it's best to focus on actually preventing it, rather than on keeping your own hands as clean as possible. (And realistically we're talking about working for an oil company or a casino or something, not being a Nazi prison guard.)

Maybe the adherents you mentioned are? I'm missing the requirement that the advice apply to "all of us".