Was president Truman right in limiting the objectives of the Korean War?

On June 27, 1950, President Harry S. Truman announces that he is ordering U.S. air and naval forces to South Korea to aid the democratic nation in repulsing an invasion by communist North Korea. The United States was undertaking the major military operation, he explained, to enforce a United Nations resolution calling for an end to hostilities, and to stem the spread of communism in Asia. In addition to ordering U.S. forces to Korea, Truman also deployed the U.S. 7th Fleet to Formosa (Taiwan) to guard against invasion by communist China and ordered an acceleration of military aid to French forces fighting communist guerrillas in Vietnam.