We really do not know the definition of natural born citizen.
Perhaps this author defines the term when he states Polk is the first natural born citizen elected President.
Polks parents were born in the Unites States.
Polk was born in the United States.
There is nothing about the circumstance of his birth or his parentage that would put his being a natural born citizen in doubt. There have been no Presidents in doubt as far as eligible citizenship status with the exception of Chester A. Arthur, who went to great lengths to conceal his father’s lack of naturalized citizenhip at the time of his birth, and Barack Hussein Obama, II, who has a whole ‘nother set of smoke and mirrors going on, to keep focus on the giant game of “Where’s Waldo” over a piece of paper, when in fact he has the same problem that Arthur went to such lengths to obscure.
His parents were born in the British North American colonies and where thus natural born British Subjects. But they became citizens of the US upon the Independence of the United States, and were certainly citizens when he was born. So yes he had two citizen parents. He was born in the country. So he was a natural born citizen.