Presumably you are referring to the creation of the Confederate government as "trying to kill the government" in Washington DC.
My understanding of history, and correct me if I am wrong, is that they wanted to separate from the Washington DC government, not destroy it.
It's an important distinction. Right after the First battle of Bull Run, the Confederates could have taken Washington DC, but they made no effort to do any such thing. They simply wanted to repel the invaders.
In any event, the CSA was free to award their soldiers whatever they want.
“My understanding of history, and correct me if I am wrong, is that they wanted to separate from the Washington DC government, not destroy it.”
You’re right. “All we want is to be left alone.” The Confederates had no wish to overthrow the US government.