If that were the case, the Founders would not have bothered to change the original proposed presidential eligibility requirement of 'born a Citizen' to 'natural born Citizen'.
Natural law is clear about who is a natural born Citizen - those born in the country to Citizen parents.
The Laws of Nature and of Nature's God: The True Foundation of American Law
You might want to wish that were true, but British law had long been accepting the dual sources of citizenship: location or blood. The children born overseas to British citizens were themselves British citizens.
It is from this that our own law is derived.
Representative Burke in the Congressional minutes regarding naturalization in the original, very first Congress: “The case of the children of American parents born abroad ought to be provided for, as was done in the case of English parents, in the 12th year of William III. There are several other cases that ought to be likewise attended to.”
Representative Hartley in those same minutes: “he had another clause ready to present, providing for the children of American citizens, born out of the United States.”