Subject's scholars & practitioners seems to disagree with your statement. Studies shows that even a limited nuclear regional war - e.g. India vs Pakistan conflict, a scenario dire enough to have about 20 million people dead due to bomb blasts and subsequent fires and radiation - could have consequences on a global scale due to a global cooling of about 1.25 °C (average) by killing crops & possibly starving about 1 billion people worldwide. A regional nuclear war could cause widespread loss of life even in countries far away from the conflict.
And today's nuclear weapons are much more powerful, when compared to those bombs which were dropped in Nagasaki and Hiroshima in 1945. The radiation will spread for thousands of kilometers (just like the Chernobyl incident, which caused a sharp increase in cancer rates in countries such as Sweden and Finland, which were far away from the nuclear plant).