Oddly enough, they stopped the first Terminators but Skynet appealed to the Ninth Circuit Court and won a decision that they have the right to kill all humans.
Well. the Constitution is a living document. It turns out that the "Right to Kill All Humans" was part of original intent.
Funny thing is, you're not that far off. In S.M. Stirling's TERMINATOR novels, Skynet's "processing" centers and weapons labs are staffed with radical leftists who believe that Mother Earth would be much better off without so many people around to ruin her.
-Dan