The common thread in both cases is (as you say) children: in both creoles and NSL, the early versions of the language are somewhat primitive (being developed by older children and adults), but when children are exposed to it from an early age, the languages acquire much more complexity and sophistication, becoming every bit as rich as "regular" languages. It fits well with the hypothesis that the early years of life are crucial for language development, and that there is indeed something innate in most humans for deep structural understanding of language. It's not just statistical pattern recognition.