That has always been one of the most basic requirements in my understanding.
Now, if the state in question is in insurrection, or the leadership has been wiped out by the disaster and is unable to request the assistance, that would be a different matter.
In this case we have a governor, IMHO, who is 1st, unable or unwilling to make the forthright necessary decisions, and, 2nd, who is playing political blame games with it and therefore with the welfare and lives of her citizens.
The State did ask for assistance. I posted the relevant quotes here:
http://www.freerepublic.com/focus/f-bloggers/1478195/posts?page=178#178
So category (2) actually does apply. But even in the absence of the state's request, category (4) can be used. It says the DHS Secretary is in charge if:
(4) the Secretary has been directed to assume incident management responsibilities by the President