My argument would be that it's not so clear cut between sincere and fake emotion. We all have dammed rivers of unexpressed emotion within us, to the greatest extent in the most repressive societies (whether religiously, politically or socially repressed). Repressed societies (like Britain) offer approved channels and safe ways to express emotion, and I think people unconsciously find their relief by projecting or anchoring inchoate and shameful feelings onto public symbols.
It's tempting to think that Koreans are play-acting, and conscious of an explicit rift between their real and fake emotions - and that because we don't experience such a conscious rift, our own emotions must be sincere in contrast to theirs. On the other hand, I am not claiming there is no difference between our experience and theirs - whatever its faults we surely live in a much healthier society.
I'd say it's good to be close enough in touch with your own feelings to be aware that you are repressing them, or faking them. But I think it's also quite painful to maintain an inner life which is at odds with what is socially approved.
A related phenomenon is belief. It's easy (I think) to mistakenly assume there are true beliefs and fake beliefs. That if someone says 'I believe x' there are two distinct states, which are exclusive and exhaustive. That is, you must be in one or the other state, and you can not be in both. The two states being that you really believe x, or that you are telling a lie.
But I think that - just like the fake/sincere emotion attending Kim Jong-il's death - there are beliefs which function as emotional pretext or symbol, but are not 'lies' as such. For example Slacktivist has written several times about The Satanic Panic around Procter and Gamble (see one post here and here is the same story on Snopes). The alleged belief is that P&G are Satanists, and reveal this by having a picture of Satan as their corporate logo. Satanic Panics in general occupy this strange zone of semi-belief. The Australian dingo-baby case, in the news today, is another example (I am thinking specifically of people who said the mother killed her daughter in a Seventh Day Adventist death-ritual). And - wildly on the edge - UFO abduction reports include a proportion of sincere delusions, a proportion of deliberate lies (I imagine), and a proportion of these strange half-sincere half-beliefs.
In all these cases people talk as if there are only two possibilities - you either sincerely believe what you profess, or you are lying. But I think this muddies each case, because people forcefully reject the idea that they are lying, they know they are not lying, and so they get locked into assertions that they must know at some level are not sustainable, but they can't let go.