You need to recall the elections of the following presidents, then. They all had at least one parent that was not a citizen, one of them had *two* foreign parents, but was born in the US.
Andrew Jackson
Thomas Jefferson
James Buchanan
Chester Arthur
Woodrow Wilson
Herbert Hoover
Every President born before the adoption of the Constitution in 1787 was
eligible because of the grandfather clause of Article 2, Section 1:
"No person except a natural born Citizen,
or a Citizen of the United States,
at the time of the Adoption of this Constitution, shall be eligible to the Office of President;"
Both Andrew Jackson and Thomas Jefferson are covered by that clause.
James Buchanan's father emigrated to the U.S. from Ireland in 1783.
When the U.S. Constitution was adopted in 1787 (and ratified in 1788),
it conferred citizenship upon everyone living in the States.
Therefore James Buchanan's parents were citizens of the United States
when James Buchanan was born in 1791. So, James Buchanan was a natural born citizen.
Woodrow Wilson's mother became a U.S. citizen by Congressional act in 1855.
Wilson was born in 1856. Therefore, both of Wilson's parents were U.S. citizens,
which makes Wilson a natual born citizen.
Herbert Hoover's mother became a citizen in 1870 under the same 1855 Congressional
act that conferred citizenship on Wilson's mother. Hoover was born in 1874 to
two U.S. citizen parents and he is therefore a natural born citizen.
Chester Arthur is a different story. So, I'll refer you to this site for the details: (more later)
http://naturalborncitizen.wordpress.com/2008/12/10/a-little-more-on-chester-arthur-from-the-library-of-congress/gottaGet2Bed!