Parents born in a foreign country could still be Naturalized as citizens. I have not done any research into whether or not their parents became Naturalized before their future president kids were born so take that for what it is worth. The children of Naturalized citizens can be a Natural Born Citizens.
Chester Arthur got away with it. But his actions of trying to hide all of his records showed that he knew that he did not meet the eligibility requirement to be VP or POTUS.
I believe Mrs. Hoover and Mrs Wilson became citizens upon marriage to a US citizen given the laws at the time.
see
http://www.rochesterconservative.com/blog/the-natural-born-presidency/
So Chester Arthur got away with it. BHO will not.