You probably know more about the CW than I do (no doubt about that), so what makes you say this? Is it conceivable that the South could make the same claim against the North, as far as which of them was fighting for the rightful meaning of this nation?
The southern states (at the time, because today, no southern state really can say they are all for states rights in the same capacity or they will give back their welfare money and their military budgets) will surely and rightfully have a point in saying that they were the ones who valued the constitution, and to be completely fair, they would have a valid point, however, they couldn't fight the machine that was the north in the long run and they lost.
That's how it goes right?
Victors write history. It's not fair, but it is what happens.
We can split out right vs. wrong or cause vs. effect, but ultimately, it's about winner vs. loser.
The CSA happened to lose, and with that, they are forced to submit to the will of the USA as the victor.