It's a somewhat minor point that I believe only supports your main argument, but this is not speaking strictly correct. From its inception in 1947, CIA has had at least two official missions: 1, the collection of intelligence (under what was first called "Office of Special Operations"); 2, "action" (under what was first called "Office of Policy Coordination," & has changed and mutated several times since), the definition and limits of which have always been a huge problem. Essentially, or at least arguably, #2 allows for military action outside the military chain of command, though not inside the territorial US. This in itself is a holdover from the OSS and other earlier orgs, all of whom had similar mandates, and even from the personnel who were part of those earlier orgs and wanted to continue their fun & games. In many ways it is #2 that is the real problem, though one could argue that the need for intelligence collection outside the military chain of command is itself debatable (MI6, the "british equivalent" of CIA in most brief descriptions, is part of the British military). At any rate, their official mandate has always been much larger than intelligence gathering. See
https://en.wikipedia.org/wiki/History_of_the_Central_Intelligence_Agency