The flag being hung next to the SC statehouse isn't even a historical Confederate flag.
Yes it is. South Carolina regiments fought in the Army of Northern Virginia, and its square battle flag is the one that was adopted by Confederate veterans groups, both those consisting of actual veterans and of their descendants. Even the rectangular flag that flew from the dome for around forty years has some historical value, tho not nearly as much as the square. It's true that neither version was a national flag, but it's official purpose as it is currently flown on the grounds is not as part of a memorial to the Confederate nation but to the Confederate soldiers.