You're right that's exactly what it means. However, there's a ton of spin going on with BS like the lost cause that try to spin the founding of the Confederacy as something morally just and even heroic. They focus on things like states rights, chivalry, rebellion (the rebel flag), etc. Of course those obviously come at the expense of truly local rights and the rights of women. If you read any of the speeches of the time or the actual articles of succession it will become very obvious that it was about slavery.

It doesn't help that pop culture leaned into presenting Confederate symbolism as "they're trying to morally rebel against the corrupt government" for a bit. That's a big reason why the Dukes of Hazard car, the General Lee, had a Confederate flag on the roof.