> My interpretation was that "the rest of the world" is meant to refer to "the rest of the countries in the world" not "the rest of the people in the world".

Even by that measure it is false. The only continents less violent than the one the United States resides are Europe, Oceania and Antarctica. The United States isn't even the most violent country in its own continent, that would be Mexico.

So really the unnecessary qualifier should be: "Well it might be bad in the U.S., but in Europe, Oceania and Antarctica..."