My understanding of this case is that it is not as simple as the article infers.
These letters had been part of the official correspondence of the State of South Carolina. The letters were part of a group of documents that were entrusted to a CS government official for safekeeping near the end of the war. His job was to prevent these and other documents from falling into enemy hands so they could be returned to the government once a safe location for their storage could be found. The letters were never the "private" property of the person who held them.
Since the war ended shortly thereafter, the documents remained with the man who had been entrusted with them. He kept them hidden from the Federal authorities who most certainly wanted to investigate them as part of the compilation of the Official Records of the Rebellion.
The letters remained hidden and presumed lost until some of them were offered at auction. That is when the State of South Carolina stepped in, arguing that the letters were state property and that they never had officially deassessed them.
I don't neccessarily agree with the decision but with the added information, it makes more sense.
If that's the story, then the judges decision was the correct one. If your grandfather is in possession of stolen property and passes it on to you, that inheritance doesn't make the property any less stolen.
In this case, the guys ancestor was entrusted with state property to protect it from the union army. When the war was over, the guy should have returned the papers to the state. The fact that he didn't makes him a thief, and doesn't grant his descendants any kind of claim to the papers.