It's irrelevant. In a world of world-destroying technologies, a really bad thing happening for only a small amount of time is all it takes. The Cold War wasn't even close to the horror of Nazi domination (probably)--there were still lots of happy people with decent governments in the west! But everyone still could have died.
What if Nazis had developed nuclear weapons? What if the AI self-reproduces, without self-improving, such that the Big Bad they're supporting has an army of super-efficient researchers and engineers? What if they had gotten to the hydrogen bomb around the same time the US had gotten the atom bomb? What if the Big Bad develops nanomachines, programmable to self-replicate and destroy anyone who opposes, or who passes a certain boundary? What kind of rebellion or assassination attempt could stand up to that? What if the humans want the AI, rather than another human, to be the leader of their Big Bad Movement, making their evil leader both easily replicable and immune to nanomachine destruction?
Hell, what if the AI gets no more competent or powerful than a human? It can still, in the right position, start a thermonuclear war, just the same as high-level weapons techs or--hell!--technical errors can. Talented spies can make it to sufficiently high levels of government operation; why couldn't a machine do so? Or hire a spy to do so?
And if the machine thinks that's the best way to make people happy (for whatever horrible reason--perhaps it is convinced by the Repugnant Conclusion and wants to maximize utility by wiping out all the immiserated Russians), we're still in trouble.
However, if you're trying to describe an AI that is set to maximize human value, understands the complexities of the human mind, and won't make such mistakes, then you are describing friendly AI.
Edit: In other words, I contend that the future threat of General AI is not in modifying humans with nanotechnology. It is in simple general ability to shape the world, even if that only means manipulating objects using current technologies. If we're defining "intelligence" as the ability to manipulate atoms to shape the world according to our bliss points, a machine that can think thousands of times faster than humans will be able to do so at least hundreds of times better than humans. This is especially true if it can replicate, which, given this hypothesis, it will almost certainly be able to. If we add intelligence explosion to the mix, we're in big trouble.
You're missing the point of talking about opposition. The AI doesn't want the outcome of opposition because that has terrible effects on the well-being its trying to maximize, unlike the nazis. This isn't about winning the war, its about the consequence of war on the measured well-being of people and other people who live in a society where an AI would kill people for what amounted to thought-crime.
...And if the machine thinks that's the best way to make people happy (for whatever horrible reason--perhaps it is convinced by the Repugnant Conclusion and want
I put "trivial" in quotes because there are obviously some exceptionally large technical achievements that would still need to occur to get here, but suppose we had an AI with a utilitarian utility function of maximizing subjective human well-being (meaning, well-being is not something as simple as physical sensation of "pleasure" and depends on the mental facts of each person) and let us also assume the AI can model this "well" (lets say at least as well as the best of us can deduce the values of another person for their well-being). Finally, we will also assume that the AI does not possess the ability to manually rewire the human brain to change what a human values. In other words, the ability for the AI to manipulate another person's values is limited by what we as humans are capable of today. Given all this, is there any concern we should have about making this AI; would it succeed in being a friendly AI?
One argument I can imagine for why this fails friendly AI is the AI would wire people up to virtual reality machines. However, I don't think that works very well, because a person (except Cypher from the Matrix) wouldn't appreciate being wired into a virtual reality machine and having their autonomy forcefully removed. This means the action does not succeed in maximizing their well-being.
But I am curious to hear what arguments exist for why such an AI might still fail as a friendly AI.