He's an actor, right?
He claims the flag represents the indomitable spirit of independence, as well as the values of the rural South, including courage, family and good times. He just didn't include all of the values of the rural South, like slavery and racism, and he didn't mention that the "good times" were pretty much any time before 1960 when blacks knew their place and stayed there.
To some people in the South, likely many of them younger than 50 or 60, who are oblivious to why the flag was resurrected in the midst of the fight against integration and Civil Rights, they may very well believe the flag represents exactly what ol' Cooter says it does, and for many of them it actually does. But Cooter is a former Congressman from Georgia, and he knows exactly what was stated in the Georgia Articles of Succession as to why Georgia was succeeding from the Union, and it mentions slavery as the primary reason for wanting to keep their State's Rights, and he knows the Confederate Battle Flag was the symbol of that fight. He wants to the flag to represent one thing, and while it does genuinely represent that, he wants to pretend it doesn't also represent the racism.
That's like flying a flag with a swastika, claiming it doesn't mean support of Nazism and the Holocaust, because it really means something sacred in Navajo healing rituals, or "peace" to the Sioux, or a "good harvest" to the Cherokee.