In the case of China the USA did commit a highly aggressive act. You have to remember that for China the war did not start when North Korea invaded South Korea it started when the USA had counter invaded North Korea and were very close to the Chinese border. Now they could view that as a highly aggressive act since at the time the USA did not recognise China and instead continued with the idea that Taiwan was the legitimate government of a China. Also China had warned the US to not put any US troops above the 38th through Indian diplomats. The US ignored those warnings and paid the price. Now whilst the North Korean version if the war is ludicrous the Chinese view is less so. There is a way to view the events that lead to the Chinese intervention as American aggression. Basically what you have done in looking at the war is focus on the whole thing the Chinese on the other hand only start to really care when North Korea started to look like it would lose and China would never want US troops on the Southern border of China and they made that point very clear and in their view America ignored it thus were the aggressors.

I was once a public historian specializing in the Korean war for a museum back in the U.S.

From China's perspective, the crossing of the 38th parallel, which was where the border had been drawn prior to the war, was regarded by China as an act of aggression against their ally. Furthermore, when the Americans (read: U.N.) crossed the Yalu River on the Northern end of North Korea, which (along with most of present day North Korea) has historically been Chinese territory for nearly a millenia anyway, this act of aggression against an ally turned into an act of war immediately.

Hence, The War to Resist U.S. Aggression and Aid Korea.

edit: as for the second part of the question, it's kind of i plied earlier when I mentioned how North Korea had been Chinese territory historically... it's easy to see how the Chinese government can justify their response to the big bad Western aggression into their ethnic homeland.

One way I've heard it said is: What would the US do if a foreign military began a war in Mexico, who didn't recognize the US as a nation, whose army was led by a general who openly wanted to attack the US, and who began bombing border towns in Texas?