Let's take a look at something that actually happened in August 1976. Two US Army officers were murdered over a tree at the Joint Security Area at P'anmunjom by the North Koreans.
We (US/ROK) locked and loaded. How do I know? I was there. A few days later we came in force to cut the tree down. Just behind the JSA we had helicopter gunships in the air, ready to blast the North Koreans. There were plenty of reinforcements available should the NKs have started a fight. We had B-52s in the air over Korea, fully bombed-up. In short, the North Koreans knew we meant business.
Kim Il-Song backed down. We removed the tree. Later a raised concrete strip was built, separating the two halves of the JSA.
Here's an account by another person who was there at the time, rather closer to the action than I was.
http://www.military.com/HomePage/TitleHistories/1,10982,100001|854374,00.html
But yes, we would have fought in 1975, and we and the ROK would have won. Korea wasn't Vietnam, then or now. Two different places. Two different mindsets.