"People use armed force all the time with their neighbors."
This was not phrased correctly. It should have said, "used," and it should have included the threat. Back when governments were weaker and there was more crime and fewer educated people, courts weren't great at punishing violence, so violence and the threat thereof were widespread - look at the historic power of organized crime. This remains true today, but it's less true because our ability to enforce the law has improved.
People used violence when it was effective and they wouldn't get in trouble with other, more powerful people. Nations used violence when it was effective and they wouldn't get in trouble with other, more powerful nations. Nuclear weapons simply changed how much trouble they'd get into, just as better law enforcement monitoring and a lower general crime rate, and falling cultural acceptance have changed how likely people are to get into trouble when they use force. I really don't think the two examples are as different as you claim they are.
Nations used violence when it was effective and they wouldn't get in trouble with other, more powerful nations. Nuclear weapons simply changed how much trouble they'd get into
The major change that nuclear weapons have brought to international affairs is not that the weaker party in a conflict gets into more trouble, it's that the stronger party does too. There is not much to be gained from fighting a war when, even if you win, your major cities are destroyed.
As Eliezer and many others on Less Wrong have said, the way the human species rose to dominate the Earth was through our intelligence- and not through our muscle power, biochemical weapons, or superior resistance to environmental hazards. Given our overwhelming power over other species, and the fact that many former top predators are now extinct or endangered, we should readily accept that general intelligence is a game-changing power on the species level.
Similarly, one of the key ingredients in the birth of the modern era was the discovery of science, and its counterpart, the discovery of the art of Traditional Rationality. Armed with these, the nations of Western Europe managed to dominate the entire rest of the world, even though, when they began their explorations in the 15th century, the Chinese were more advanced in many respects. Given how Western Europe, and the cultures derived from it, has so completely surpassed the rest of the world in terms of wealth and military might, we should readily accept that science and rationality is a game-changing power on the civilization level.
However, neither of these imply that intelligence, science, and rationality, as a practical matter, are the best way to get things done by individual people operating in the year 2009. We can easily see that many things which work on the species level, or the civilization level, do not work for individuals and small groups. For instance, until the discovery of nuclear weapons, armed conflict was often a primary means of settling disputes between nation-states. However, if you tried to settle your dispute with your neighbor, or your company's dispute with its competitor, using armed force, it would achieve nothing except getting you thrown in prison.
People are crazy and the world is mad, but it does not necessarily follow that we should try to solve our own problems primarily by becoming more sane. Plenty of people achieve many of their goals despite being completely nuts. Adolf Hitler, for example, achieved a large fraction of his (extremely ambitious!) goals, despite having numerous beliefs that most of us would recognize as making no sense whatsoever.
We know, as a matter of historical fact, that Adolf Hitler and his Nazi Party, despite being generally incompetent, unintelligent, irrational, superstitious and just plain insane, managed to take over a country of tens of millions of people from nothing, in the span of fifteen years. So far as I am aware, no group of people has managed to achieve anything even remotely similar using, not only rationality, but any skill involving deliberative thought, as opposed to skills such as yelling at huge crowds of people. However, it is a corollary to the statement that no one knows what science doesn't know that no one knows what history doesn't know, so it is entirely possible, perhaps likely, that there is something I am overlooking. To anyone who would assert that intelligence, science or rationality is the Ultimate Power, not just on the level of a species or civilization, but on the level of an individual or small group, let them show that their belief is based in reality.