With such assurance, I assume you were there and know for sure. However, you apparently forgot to inform some of the black CSA soldiers. See http://blackconfederates.tripod.com/
I don't know whether the information on the above site is correct or not, but I would be very surprised if there had never been any black CSA soldiers. Not many, but some.
In the oral history of one branch of my family, slaves buried the family silver and saved it for the family when Sherman's troops came through South Carolina stealing food and valuables. Not all of Sherman's troops stole, of course. A small band of them rode up to my wife's great-grandmother's house (my wife's great-grandfather was away at the war). The soldiers were very polite to the young woman and her small children -- they asked for food and shelter for the night. They were given food and allowed to sleep in the barn.
Hmmm...would you say that whatever black soldiers there were had the same civil rights as white soldiers?
If not, that is a blight on the so-called seceded states isn't? Doing so poorly for the men who fought for them?
Walt