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.
Stand Watie is a legendary hero in the Eastern Indian community.
My great, great, great uncle commanded a Creek confederate unit. They didn’t see a lot of action. But he left voluminous diaries of every day life in an Indian confederate unit. After the war there was no authority to discharge him and his men, so he wrote his own discharge papers.