Bush requested and obtained revisions to that section of law. The feds now have the power to insert themselves without a request from a governor. IOW, the feds decide what constitutes emergency, and the feds self-declare the circumstances as warranting the use of federal military troops to handle the situation.
For all his other faults Bush did that in part because of the fiasco in New Orleans where the governor refused to let federal assistance that was mobilized and ready to come in to help until she knew it could be blamed on Bush. FEMA and the administration did the right things to try alleviate the problems but they screwed up by accepting blame for FEMA who did nothing wrong.