Pieced this together. Has to do with the ability of non-state police to conduct police operations, including arrest, and a requirement to bond them.
Without that, Federal entities and National Guard troops are powerless to do much of anything to restore order except shout "hey" as someone rolls on by doing whatever.
So, I will concede that it didn't request Federal assistance, per se, but what it did do is nonetheless quite important in the scheme of things--it allowed the Federal assistance to be effective. Until then, not much could go on because control was still retained in the, by then, vastly overwhelmed local authorities. This declaration changed the equation, but it didn't show up until storm-day plus three. (Fine point, it was signed the evening before, but really didn't become a practical instrument until Sept. 1.)
You mistake the general effect of this order.
There are regulations for actors to be admitted to be under Blanco's control as LEO's. This order relaxes parts of those regulations, and therefore made it easier to obtain LEO under "her" control. It most likely smooths the way for actors who are LEO in extra-LA jurisdictions.
At any rate, the order has ZERO relationship to federal action.
A separate writing, which we have not seen, empowers NG activity (which, FWIW, is not federal action in the context of disaster relief).
And yet again another separate writing, which we have not seen, empowers active-duty military to perform evacuation activity.