It was also not his Presidency that ultimately ended the war, or gave us the Cold War (which rightly should be called World War 3). Truman gave us both of those, good and bad. The end of WW2 was the result of the inertia of the Manhatten Project, not any brilliance on Trumans part (though it was both gutsy and right to make the call). The cold war, including the stalemate in the battle of Korea and the loss in the battle of Vietnam, is directly attributable to the inertia of a failed liberal Presidency of a small, if tough, little man.
When the Soviets sealed off west Berlin in 1948 and some advocated ceding Berlin completely to them Truman took a stand for the west and ordered supplies to west Berlin to be delivered by the Air Force. Truman asked the generals if they could keep up supplying west Berlin, to which the generals answered they could do so indefinately and then Truman told them to step up their efforts and that he would never cede west Berlin to Stalin. Truman also kept Turkey and Greece out of Soviet clutches with his doctrine. And the loss of mainland China to the communists had to do with the massive corruption in the nationalist Chiang government, not failed Truman policies. Saving China from the communists would have taken a field army larger than the one deployed in Europe. North Korea invaded the south encouraged by the Chinese communist success, and only timely action by Truman recalling MacArthur saved South Korea for the west. It would have been a complete victory and a complety reunited western Korea if it hadn't been for the interference of the Chinese army.
France, in an attempt to keep the Indochinese colony (which included Vietnam) decided to fight for their former colonial holdings thus triggering communist/anti-French anti colonial forces to combine forming the Vietnamese Liberation Army (later the VC). After a humiliating French defeat at Dien Bien Phu Eisenhower (who was president) decided to send "advisers" to help keep south east Asia out of communist clutches.
To all of the valid points you make about Truman, including Berlin, Greece, etc., I still stand by my summary of his administration:
a failed liberal Presidency of a small, if tough, little man.
His actions may have been the only choices, in each case, but they were the actions and choices of a failed policy, not a winning policy. The Truman administration didn't win anything. At best it can be argued that they set the stage for the winning of the "long struggle" some 40 years later. Others would argue that his failures and inadequacies led to 40 years of corruption and the imprisonment or death of millions. We can never know. We do know he didn't win anything while he was President based on his own policies (except his defeat of MacArthur... great legacy).