Those requirements boil down to this:
- One parent must be a citizen.
- That parent needs some connection to the US, measured by how much time they've spent living there.
- If the citizen parent is male, he must prove that the child is related to him.
- If the citizen parent is male, he must swear a binding legal oath to financially support the child.
The rest resolves these questions:
- How much residential connection to the US must citizen parents have, based on the couple's total Americanness? (more Americanness, less time)
- Can we just assume that married men are the fathers of their wives' children? (yes)
- What counts as being "in America"? (government service abroad counts)