What was America's involvement in the Korean War?

America brought the topic of Korea to the UN when the USSR was upsent (as a protest for the Chinese Popular Government, which hadn't been given a seat. Instead, it had been ocuppied by the Chinese capitalists that had flown to Taiwan with help of the US). Moreover, it convinced the rest of the countries to organize a defensive army to help South Korea from the North Korean invasion.

The thing is, this troops responded to the American President Eisenhower instead of responding to the UN, its commander was American and most of the troops (approx. 50% of the land forces, 80% of the aircraft and also the navy) were sent by the USA.