That is BS. The SCOTUS, if it had ruled that secession was illegal AFTER the Civil War, would have made the South totally within its Constitutional rights to secede. The US Constitution is silent on the issue of secession, and will remain so forever.
President Davis asked for a trial after the war but was denied a trial. Nobody wanted to put him, and secession, on trial. Everyone knew that would be a losing case and secession would be found Constitutional.
"When, therefore, Texas became one of the United States, she entered into an indissoluble relation. All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration, or revocation, except through revolution, or through consent of the States.
"Considered therefore as transactions under the Constitution, the ordinance of secession, adopted by the convention and ratified by a majority of the citizens of Texas, and all the acts of her legislature intended to give effect to that ordinance, were absolutely null. They were utterly without operation in law."