Hilter was democratically elected as well
My beliefs changed a lot once that I read Natan Sharanksy's book "The Case for Democracy".
From that book, just because there's a "free" vote doesn't mean that there is a democracy because the institutions are not in place so that people can be free. Clearly, the institutions in "Palestine" and Iraq did not meet that minimal criteria.
I am sure that Bush knows this because it was one of his favorite books and he invited Sharansky to the White House. I am guessing that he figured that these forced elections before the foundation for democracy existed was better than having nothing.
It's not a perfect world.