The closest example I can give is that I work on a system where the birthday can be partially unknown. This mostly affect refugees. So the person either has to guess his own age, or only knows the year, or only the year and month.

Then again, someone might make a mistake. "What do you mean 09-11 is not November 9th, you silly American."

Now that I think of it, I guess the best argument against natural keys is "typos".