I like this way of approaching the problem, but I don't think it convincingly contradicts the GP's point; if participants were just entering invalid data to ski

I like this way of approaching the problem, but I don't think it convincingly contradicts the GP's point; if participants were just entering invalid data to skip the question, then I think they would enter a similar type of number in both "# older siblings" and "# younger siblings", e.g. 0 and 0, or 100000 and 100000, or `rand(10)`. The key observation is that I'd expect the same RNG to be used for each of the four fields. I think you'd see much more `0`s in the fake data as well (it's a Schelling point). But if the fake-data population was disproportionately recorded as only children, that would have reduced the first-child effect, not attenuated it.