So let's dispense with the canard the U.S. is concerned with the sovereignty of any foreign government or its people's antipathy toward the United States for actions we initiate.
In America, it's all about American domestic consumption (how it plays in Peoria) and fending off potential right wing attacks of being "soft"" on defense, terrorists or formally the old bogeyman "Communists".
So what if a U.S. led clandestine special ops raid in Libya could cause a backlash among the Libyan people and the government of that country.
Just remember, it won't matter if we kill a few Libyan's regardless of whether or not they were involved in attacking the U.S. mission in Benghazi. Our policy is to attack and kill first and if we subsequently find out later they were innocent well just offer condolences, maybe pay blood money to the families who lost a son or a father or more likely chalk it up to "collateral damage" i.e. sorry, but they were in the wrong place at the wrong time.
When a country loses its moral footing and easily rationalizes the killing of innocents, torture, holding suspects indefinitely, orders the assassination of anyone, even American citizens without consideration of due process, there's really no limits to the extent of what it is prepared to do.
Besides, after the fact of some clandestine operation, all that's necessary is just issue some dissembling nonsense to the fawning MSM to foist upon the American people.
Empires and a world wide hegemonic power like the U.S., doesn't see a need answer to anyone; except in those instances where actions are taken just to keep the right wing nuts at bay.