The Supreme Court decided otherwise in 1862.
See The Prize Cases.
Walt
The Supreme Court also decided the Dred Scott Case. Every time the Supreme Court reverses itself on a constitutional question, it acknowledges that its prior decision was unconstitutional.
The Supreme Court may be the final arbiter of the Constitution but they are not omnipotent.
They didn't say that secession was illegal, they said "[t]heir right to do so is now being decided by wager of battle."