I think that phrase sums up your argument. And I would add that it represents your thinking only. It is your concept of the Constitution only. It does not reflect the thinking or law of the time.
You are wrong to perfection. At the time of secession, the Executive, the legislative, and the judiciary all agreed that secession was not prohibited by law.
Secession was prohibited by the nature of the Union and the logic of the constitution. Not to mention the words of the document itself: Article III, Section 3, paragraph 1 - Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them aid and Comfort.
If the Cornfederates weren’t committing treason the word has no meaning whatsoever.