I know there's another thread on this, but my question is a little more nuanced.
If an American born and residing couple adopt a child from another country (say Russia), that child receives a new Amended Birth Certificate once the adoption is complete. That Birth Certificate will have the child's new name and new parents name listed and will be issued in the county the adoptive parents are living in. So, for example, this Russian born child will have a Cook County IL Birth Certificate with his/her American parents listed as the mother & father.
What's to stop this person from running for President some day? The Birth Certificate doesn't say "adopted", it just says he/she was born in Russia. It doesn't say one way or the other if the mother literally gave birth to the child. Children born to American parents traveling in Russia are still natural born American citizens and their Birth Certificate would look the same as this adopted child's birth certificate. Couldn't the adopted child just say they were born to parents travelling in Russia?