What explanation is needed?
He was the first elected President to be a natural born citizen. (John Tyler was the first President to be natural born, but he wasn’t elected President, he was elected Vice President and became President when William Harrison died in office).
Until Tyler, all U.S. Presidents were botn before the Constitution was ratified, thus they fell into the “or a Citizen of the United States, at the time of the Adoption of this Constitution” clause.
How does President Polk compare to Obama. Seems Obama must match equally to Polk in order for Obama to be a natural born citizen.
Polk had two US citizen parents. Obama does not.
To determine what the author's understanding of what the term "Natural Born Citizen" meant. Presumably, he (the author) was using Vattel's definition...really the only known definition for that "type" of citizen, in 1787.