This simply isn't true.
All children born in the country were "natural born subjects," whether their parents were English (or colonial) or not.
There's a pretty extensive discussion of this in the majority opinion of US v. Wong Kim Ark (1898). Anyone can read it for himself.
The same rule applied in the Colonies and in the United States after the Constitution was adopted.
Therefore every person born within the United States, its territories or districts, whether the parents are citizens or aliens, is a natural born citizen in the sense of the Constitution, and entitled to all the rights and privileges appertaining to that capacity. - William Rawle, A View of the Constitution of the United States (1829)
Rawle was one of our most prominent early legal scholars, and a close associate of George Washington, Benjamin Franklin, and several other Framers of the Constitution.