In the incident which you cite, FEMA turned it down because it wasn't considered to be a major disaster - i.e. one that the combined resources of the state and local authorities weren't equipped to handle.
It's not any different than any other relatively minor event that can be handled at the local level.
That is quite a bit different than believing that a well funded national disaster preparedness system is unnecessary for major disasters that are beyond the capability of state and local authorities which is what Romney and Ryan have espoused. Ryan, while in Congress, voted to defund FEMA.
“We evaluate the need,” Edwards said in an interview last week, adding that the agency then weighs the need against what it determines are the combined abilities of local government, state government and any private, community and volunteer organizations to respond to the crisis.If FEMA decides that a disaster’s overall impact outweighs that capability, Edwards said, the agency’s regional administrators send a report to the White House recommending that the president grant the request for disaster assistance. If the agency determines the disaster does not outweigh the state’s ability to respond, the governor gets a disappointing letter, like the one McDonnell received, letting them know about the decision and giving them 30 days to file an appeal.