Pretty much everything Academi/Xe/Blackwater ever did was at the behest of the US government. GP was talking about a scenario such as Apple hiring Academi to destroy Samsung's factories.
So far we have private companies providing security/defensive services, but we have yet to see private companies providing mercenary/offensive services without the explicit involvement of a government.
The Pinkertons are considered the epitome of the "Wild West" - that is, the total lack of state control of law and order in the American West. Their intervention in strikes in the East is, to put it mildly, not a good example of law and order and a functioning state.
So far we have private companies providing security/defensive services, but we have yet to see private companies providing mercenary/offensive services without the explicit involvement of a government.