The 2011 Guardian article seems to be based very closely on an article on Matador Network, which itself is copied from an undated infographic, which lists its sources in the form of a bunch of unlabelled URLs in a horrid blue-on-blue font at the bottom. Example:
The infographic states:
His biography also says he doesn't defecate or urinate like other people.
I couldn't find an OCR accurate enough to extract the URLs so I had to type each one out manually. Eventually, by Googling instead of trying to visit the dead URLs, I figured out that the infographic originated from a 2008 blog post, which says:
Kim has schools teach people that his birth led to a spontaneous
rainbow breakout… and that he doesn’t defecate
I'm glad that post is still up, because it brought me to the next source: Wikipedia.
Wikipedia, in 2008, cited The Aquariums of Pyongyang:
Defectors[who?]have been quoted as saying that North Korean schools
deify both father and son, teaching that they do not urinate or
defecate like mortal humans.[need quotation to verify]
As you can see from the other answer, The Aquariums of Pyongyang does not make the claim that "North Korean schools" ever taught such a thing or that it was ever written down anywhere. It's purely the word of an adult defector attempting to describe the mindset of "North Korean children" or more specifically him and his friends. As I said in the comments to that answer, it's entirely conceivable that some small children think about monarchs this way in other countries as well.
By a poorly worded insertion on Wikipedia (which was removed within months) and a game of online telephone made by list writers paraphrasing each other, this florid turn of phrase in The Aquariums of Pyongyang became an actual "official biography".