Our family history shows that even a few indians, as well as blacks, did indeed fight in the Confederate army.
The pervading sense of the diaries (mostly of a Creek indian commander of an indian cavalry unit) is that the south was being invaded, and that everyone was needed to defend their farms and cities from the northern invaders.
Nobody has ever claimed otherwise, AFAIK.
Indian regiments played a key role in the Confederate defeat at Pea Ridge, for instance.
The last Confederate general to surrender, Stand Watie, was a Cherokee.