Yeah, but it stands to reason that before it was codified as a PD, it must have (or, at least, SHOULD have...) received a pass (or at least a review) from the Judicial branch.
There is a scene in the "Directive 51" book in which the lady Chief Justice of the Supreme Court is going through the new President's hastily-written speech that he is about to deliver, and she is redacting parts of it that don't jibe with PD-51, suggesting that Judicial has at least a nodding familiarity with the directive, at least in the book.
And if there is a national emergency in which PD-51 has to be invoked, I think the overwhelming feeling of the populace would be satisfaction that "someone" is in charge (even if it's the "wrong" person, in their opinion), and not too inclined to ask a lot of questions about how they got that way, especially if they're dealing with the immediate aftereffects whether it be nuclear war, some kind of environmental holocaust, or something like the aftermath of Daybreak.
When it's a struggle to find food and fresh water and keep your loved ones alive, you're less worried about politics...and those were the conditions in the "Directive 51" book.