I read on one of the many other threads that one of the additional complexities is that the LA legal and governmental system - being based on the Napoleonic Code - is entirely different from any other in the US. The powers of the officials are different, for one thing, and it is not clear that the Governor even has the power to declare martial law.
I'm sure a more resourceful one would have found a way to do so, since that was clearly what was needed, but Blanco is far from resourceful. (Possibly devious, yes, but not resourceful.)
No matter what the term of art is (e.g., LA declares "State of Emergency" which is just another word for "martial law," and even those come in any form required to get the task done then restore full civil liberties), the federal/state relationship and state-to-state relationship is independent of the in-state law.
Right now, Blanco is trying to keep the authority, but shed the responsibility.