There is NO way that the county closed the airport to DEPARTING flights.
They may have closed it to INCOMING flights but usually the airports are not closed because then NO planes can land EVEN IN EMERGENCY once the airport is closed.

For any airport authority to close an airport with hundreds of millions of dollars worth of aircraft on the ground and the storm winds not exceeding the published maximum allowable velocity for take off would make the AIRPORT/County/Taxpayers responsible for any damages to the aircraft once the storm hits.

If AIRLINES stopped bringing in flights, the airport can figure when all planes available will have left and announce the airport will close. More than likely that is what happened. United and all others knew when they were cancelling flights INTO Florida. Whether or not the reservation desk knew who knows.
But in reality it is simple no plane comes in then no plane goes out.

Was this man "taken advantage of" during an emergency ?

If he had a valid ticket out of the emergency area and their were flights with empty seats that he had to pay over $1000 additional to get a seat on that flight, I would say yes UNITED "took advantage of the situation" and for all those United can do no wrong people on this board I will bet that you would be upset if it happened to you. Policies get suspended in emergencies and it becomes a point of moving people out of the area. You move them when they show up or you move them later. To not move them the first time they show up when you have empty seats is poor business.