Just looked it up. You are so right:
Cody was born as Espera Oscar de Corti in Kaplan, Louisiana, a son of Antonio de Corti and his wife, Francesca Salpietra, immigrants from Sicily, Italy. They had a local grocery store in Gueydan, Louisiana, where he was raised.
In some of his earliest acting credits, Cody was listed as Tony de Corti. Cody was drawn to the Native American people finding comfort/similarities for himself in their struggle. He later changed his name to Tony Cody, and from then on lived his life as if he were of Indian descent, both on and off the screen.
Cody married Bertha “Birdie” Parker, a woman of Native American descent, but his “Indian” ancestry was a complete fraud.
Ah, I thought he was actually born in Sicily and immigrated to the US to be an Indian.... He was actually born in LA, interesting indeed.