It has always been my understanding that the core of the Bush doctrine was that the United States would no longer distinguish between terrorist organizations that are independent of any state or nation (e.g., Al-Qaeda) and nations that sponsor such organizations. This marked a radical departure from the previously held position, which had maintained this distinction. 

In my view, much of the confusion about the substance of the Bush doctrine results from conflating 1. the means of enforcing the Bush doctrine with  2. the doctrine itself. Reserving the right to launch pre-emptive strikes against a nation that sponsors terrorism would, for example, be one way of enforcing the Bush Doctrine. Furthermore, reserving this right already presupposes the principle that the Bush doctrine articulates.
So, although I think Palin fumbled  when she responded to the question, at the same time Gibson revealed his own ignorance when he clarified what, according to his understanding, the Bush doctrine meant.
Alexander F. Di Pippo