I don't really believe it. They don't have any reason to hide Kim Jong Il being dead unless they have no successor lined up. It's not like he is the only one behind the current state of the country so I don't really buy this.
I would have said it was an absurd theory when I first looked at the story, but then Kim Jong Il is absurd and with as screwed up as he made the country (while sure there ARE other people who've messed up North Korea, a lot of it has to do with his incompetent policies, which have more or less highlighted the danger inherent in Communism when abused), I wouldn't be terribly surprised if some fake were ruling in his stead. Anarchy is almost a given when there's a bad transition of power, and frankly NK isn't in a stable situation, to say the least.
Of course, since the theory rose up from a Japanese source, that leads to an easy way to dispute the possibility anyway. :P