There are two assumptions in this meme:
- The black confederates were a representative sample, rather than a tiny minority.
- The black confederates wanted to serve under confederate colors. Legally speaking, the confederacy drafted whites. However, given the prevailing attitudes towards black people at the time, forcing blacks to do any kind of work necessary for the war effort, fighting included, would have been natural for the confederacy. If you can draft whites, a-fortiori you can draft people who don’t have full rights.