I must wonder whether, and to what extent, these results would replicate in a real-world situation where the question is perceived as truly important by the parties concerned.

When discussing research like this, people often imagine the subjects fully applying themselves, as if they were on an important exam or in a business situation where big money is involved. However, to get a more realistic picture, you should imagine yourself in a situation where someone is asking you obscure TV quiz-style questions about things that you don't care about in the slightest, bored to death, being there only because of some miserable incentive like getting a course credit or a few dollars of pocket money. I can easily imagine people in such a situation giving casual answers without any actual thought involved, based on random clues from the environment -- just like you might use e.g. today's date as an inspiration for choosing lottery numbers.

Therefore, the important question is: has anyone made similar observations in a situation where the subjects had a strong incentive to really give their best when thinking about the answers? If not, I think one should view these results with a strong dose of skepticism.