It's extremely common for disaster response and search & rescue teams to ask random volunteers to stand down and stop trying to "self-deploy" and help on their own.
First, it's inherently a more dangerous airspace than usual, given the huge numbers of aircraft flying around, lots of low level flying, and degraded communications and other networks.
Second, just keeping coordination between all the different units, groups, volunteers, and aircraft in a mass disaster like this is a huge undertaking. There are dozens of aircraft, hundreds of distinct organisations down to local fire departments and volunteer groups, and thousands of people all of whom have to stay reasonably organised to ensure everyone who needs to be rescued is. Which is why as far as possible it's best to use only the volunteers who have not only trained in the relevant communication and coordination protocols but actually practiced them at least once. If that group is overwhelmed then they look outside and bring on others through established and expedited procedures so that they don't jam up the works.
This is one guy and his helicopter, which in the greater scheme of things isn't so bad. But imagine it's 20, 30, or a 100 all doing what he's doing.
His mistake was only coordinating with some local firefighters, and believing that was enough. But they're not in charge of air operations. He should've approached the relevant air operations cell for South Carolina, or gone via one of the established volunteer organisations for pilots with their own aircraft that have pre-existing relationships with the Air Force and other organisations involved in rescues and disaster response, and are prepared to take in new volunteers and use them effectively.