The captain and a crew member are among the boat's 28 survivors; the U.N. says more than 800 would-be migrants died after cramming themselves onto the 66-foot boat.
With record numbers fleeing the Middle East and Africa in overcrowded boats, the Catrambone family is conducting private rescue operations in the Mediterranean Sea.
Last year an appeals court overturned the seven-year sentence against the controversial former Italian leader. Judges on the Court of Cassation backed that decision Tuesday.
The High Commissioner for Refugees wants the European Union to expand its Operation Triton to intercept and rescue would-be migrants, most of them trying to reach Italy.
Captain Francesco Schettino was sentenced to 16 years in prison for his role in the disaster, in which an Italian cruise ship hit rocks in 2012 and sank, killing 32 people.
The refugees and migrants had tried to cross the frigid Mediterranean in open vessels without food and water. The estimate comes from the U.N. refugee agency, which spoke to survivors.