As a Korean living in Seoul, I'm going to chime in a little.
I have tremendous respect for American troops stationed here, especially after my conscription service. On principle I think should pull back, but if shit hits the fan, every Korean will be glad they are here. Koreans didn't complain when American troops were dying fighting the Communists.
Because the US troop issue is a major for left wing Koreans, the media and liberal politicians never miss the chance to jump over any wrong doing by American troops, and even foreigners in general. Koreans like all people, always like to blame outsiders for their problems. Due to the political pressures, the American GIs who are indicted for crimes are sometimes never even given a fair trial and the Korean public never hear the other side of the story (or don't want to). The police and judicial system is incredibly biased against American soldiers.
An American soldier will get far harsher treatment than a Korean who commits a similar or even more heinous crime. This is a country where raping a 9 year old will only get you a few years. If you're a local man. But an American soldier does anything remotely wrong, people want to see white people's heads on a spike.
That being said, some of the bad rap of them being rowdy isn't completely unwarranted. When I go to bars frequented by American GIs, I see a disproportionate number of dudes trying to look tough. That happens in any bar or club but I noticed it more with American GIs. I wonder why that is. I've met some GIs who were pretty cool once you got to know them but as a whole, they need to lighten up a bit.
As for the Psy thing, he's just a pop star who wants to be in the spotlight. Hating America was cool back then and he wasn't going to miss out on that.