If you study immigration cases, you'll find that what you say is not true. In mixed-nationality cases, it is not unusual to look at the laws of other countries, to settle the question of citizenship to the person. Of course, that is done from a basic framework of US law, but just to pick an example, the US residency requirements for a one-citizen parent vary, depending on if that citizen parent is in wedlock or not, as recognized in the foreign country. There is a pretty long string of cases "decided the wrong way" because the government misled the court about the contents of Mexico's constitution, when the controlling law (of matrimony or child-care) was actually that of a Mexican state. The outcomes of those cases are citizen vs. not-citizen.
“Of course, that is done from a basic framework of US law...”
Well, that is the key. If we pass a law that takes into account the parent’s citizenship status in another country, then the citizenship is still being determined by OUR laws, not by the other country’s laws.
If citizenship is truly based on other countrys’ laws, then what is to stop Canada from declaring anyone a “Canadian citizen” if they wish to stop them from being elected President? Absolutely nothing! Any podunk country on the planet could pass an edict and influence our elections if we did things that way.