In a pinch, a birth certificate gets the job done.
In your closing argument or statement, you are confating fact of citizenship (can't get a passport without evidence of citizenship) with source of citizenship. Bellei (and your child) were made US citizens SOLELY by dint of statutory law.
If the statute didn't exist, if there was no US embassy in Russia, would your child be a natural born US citizen? You say yes. I say no.
I'm not going to discuss this further with you, my mind is made up, and so is yours. We will never agree on this subject. You get the last word.
I'll leave you with one point: the Naturalization Act of 1790, the first statute dealing with rules for US citizenship, specifically provides that children born abroad to two US citizen parents are not only US citizens, but natural born US citizens...indeed the only time this term has ever used in statute. So, it seems that there may be room for more discussion around the argument that "natural born" == "natural law" citizenship, somehow.