After the end of the Chinese Civil War in 1949, Chairman Mao's communists controlled all of mainland China (known as the People's Republic of China) while western-supported republicans (the Republic of China) retained control of Taiwan. The RoC was given the UN security council seat of China as a way for the western allies to counter the legitimacy of the Communists and support the RoC. However, at the beginning of the 1970's many countries across the world, including many western democratic states, began to recognize the PRC as the legitimate government of mainland China. They were given the RoC's permanent security council membership in a 1971 vote, 21 years after the start of the Korean War.

To directly answer your question, The People's Republic of China could not veto UN involvement as they had no veto powers at the time. The Republic of China (Taiwan) did, and chose to support UN involvement in Korea rather than oppose it.

Hope that answered your question, sorry for going off on a bit of a tangent!