He is swearing that he believes he is a natural born citizen by virtue of (1)The location of his birth and (2)the citizenship held by his mother.
In many ways, this is quite the perfect crime. There is no way we can prove that he knows any different.
If he amended his HI birth certificate to add a birthweight (or otherwise complete it) in late 2006 before he declared that he would run it would be proof that he decided to run KNOWING he had no valid HI birth certificate and that he had either been using a fake HI BC his whole life or else he had been using a BC from somewhere else his whole life.
And it’s always the coverup that gives things away. He knew he didn’t have any legally valid documentation, or he wouldn’t have fought every attempt to require him to show his documentation. The lies about his BC being burned in a fire that never happened... it was all a big cover-up that he wouldn’t have needed to do unless he knew darn good and well that he would be BUSTED if people knew the truth.