Huh. We have seven kids. This didn't play at all into our decision on how many kids to have. Though, they were spaced out far enough that the older ones were aging out of car seats before the younger ones needed them. I don't think we ever had more than 2 kids in a carseat and 1 kid in a booster seat. We are down to 1 kid in a booster seat and the three oldest driving cars on their own now.
Your personal anecdote would be, more or less, consistent with their findings...
"there are no significant differences in birth rates when a woman has two children where just one requires a carseat."
That said, I don't think this is anything more than a correlation; not even a strong correlation (requiring many caveats, controls, and cofactors), and to me that effect size seems nominal.