Why? If Williams says that secession was legal, and that Lincoln was wrong in trying to stop it; and the Constitution flatly contradicts him -- what other argument need be made?
Because the States created the Constitution you have to determine if a State has the right to not be bound by the Constitution. The federal government was brought about by the action of independent States. If an independent State enters into a compact with other independent States, each State presumably has the right to withdraw from the compact unless it explicitly forfiets or waives that right.
There is nothing in the Constitution which prohibits a State from peacefully withdrawing from the compact.