I have been told by others (who understand this better than I) that all she requested was money, not really physical help with evacuation.
That is correct. The Stafford Act is a mechanism by which the States can request federal funding to supplement disaster relief operations. The actual physical implementation of disaster relief operations is a responsibility of the States or Territories, such as Guam and Puerto Rico. Each State or Region has a FEMA director charged with coordinating with local officials to support disaster relief functions. Ultimately, however, the disaster reponsibilities reside with local governments, not FEMA. In the case of the Gulf States affected by Katrina, the Governors of those States are responsible for actions in their States with respect to disaster operations. With the exception of the Coast Guard, all deployed active and non-active military personnel deployed to support the States to mitigate the effects of Hurricane Katrina report through the chain of command to the Governors of each State. Since the Coast Guard was transferred to the Federal Homeland Security Department previously under the auspices of the Stafford Act, they report directly to the current Director of that Department, unless they are deployed outside of US Territorial waters as directed by the President or the Congress. An exception to those general rules for example would be in the Great Lakes were we share a border and vital shipping lanes from Lake Superior to the Atlantic with Canada. Thus, Canada and the USA share responsibility for the protection of those vital assets via longstanding treaties between the two countries.