It feels that the number of 23 is specific to the context of birthdays. If it was switched to a different context such as coming from the same part of the word, or driving the same car, would the result be as surprising?
I believe statistician ecologists use the reverse in an interesting way.
Tag 100 units from a species, say goats (failure of imagination on my part) from a certain location. Then sample 100 other animals at a different time, controlling for time spent and so on, and the ratio of tagged animals that come up in the result will give statistical information about the total population of said species.