Could be wrong but I'll take a shot. The greatest good for the greatest number isn't an ethically oriented doctrine in that it allows immoral acts provided they yield more benefit than harm. For (a poor) example, say there's a town where people are being murdered and the townsfolk have become so terrified of going outside that commerce is suffering to such an extent that pretty soon there won't be any food in the store and lots of people are going to die of starvation. If we just grab some poor dude and hang him in the public square, and keep a hush on future murders, then everyone will feel secure again and go back to growing their crops or whatever and the townsfolk will be saved from starvation.
In another town where there are no murders or terrified people, it's clearly immoral to execute an innocent man. Just because there's a benefit to our town in calling an innocent guy a murderer and executing him, he's still an innocent man and it's just as crappy a thing to do here as it would be anywhere. The same applies to misinforming the people about the identity of the killer as well as about the occurence of future murders. A beneficial upside doesn't turn an immoral act into a moral one. It's still an immoral act. Just ask the innocent man.
Mill would (possibly) respond that it would be the greater evil to allow the entire town to perish rather than choose the lesser evil of executing an innocent man and misinforming the population. Not to save tens of thousands of lives by sacrificing just one would be the most immoral choice. Therefore, according to Mill, Utilitarianism does concern itself with moral action and is not simply expediency without regard to ethically motivated conduct.
