Is the LA Times Rewriting History?

In defending the practice of "leaking," the LA Times writes: "Founding Father Alexander Hamilton, whose face adorns the $10 bill, played a crucial role in winning popular support for the Constitution. But his dream of becoming president was dashed when someone told a scandal-mongering journalist about an affair Hamilton had had with a married woman. "  

… Correct me if I’m wrong, but I thought the fact that Hamilton was born in the British West Indies would have constitutionally destroyed his “dreams” of becoming president???