children of US military born overseas

The debate about what natural-born means has often been confusing to me.

The USA does both, Jus Soli and Jus Sanguinis to determine citizen status at birth. But when it's about eligibility for president, suddenly extra weight should be put on Jus Soli being the only real proper form of citizenship? That makes no sense to me.

I thought natural-born would mean citizen at birth, not immigrated and naturalized. To avoid situations where for example some English noble immigrates and naturalizes in name only, uses his wealth to gain political power, and then puts the US back under English influence. It makes sense to me that the founders of a new republic would want to avoid having it twisted by former masters.