Incorrect. The Framers were vert concnered about this. Two British “agents” could have come to America, had a child and this agent for the UK could have become POTUS. They were very paranoid about this or any dual loyalties.
Persons born in the United States, and persons born on foreign soil to two U.S. parents, are born American citizens and are classified as citizens at birth under 8 USC 1401. They are native born citizens and don't have to go through any naturalization process.
Since there is no clear cut definition of what constitutes a natual born citizen in the Constitution and there have been no SCOTUS decisions that clearly define it, I would assume that common practice and laws would heavily influence any decision. I seriously doubt that SCOTUS would try to change jus solis, i.e., birthright citizenship without any real Constitutional basis to do so. I think it would require a constitutional amendment to change it in much the same way Ireland did it.