I took the liberty of highlighting the relevant clause that seemed to escape your notice.
The ROK-US Air Component Command is responsible for the air defense of South Korea (ROK stands for the Republic of Korea), and conducting military operations in the event of another conflict on the Korean Peninsula. 7th AF has administrative and operational control of ROK-US ACC elements that are USAF units. CinC United Nations Command is responsible for the overall defense of South Korea and is headed by a US Army four-star (who also serves as Commander, Eighth United States Army). In short, the commander, 7th Air Force, is responsible to the overall military commander in South Korea for the training and readiness of all aerospace elements assigned to US Forces, Korea--which, because the defense of South Korea was undertaken pursuant to a UN Security Council Resolution, also happens to be UN Forces, Korea. Incidentally, the United Nations Command has NO responsibilities outside the Korean peninsula.
Since you don't seem to understand how the UN plays into the military situation in Korea, or how far the responsibilites of those commanders extend, how joint, specified, and unified commands are organized, and under what terms the various forces serve, your example is less than convincing.
go look that up and it will wake you up