There may be some historical backing for it, and it certainly looks like it fits to some extent with the "Scots-Irish" legend. But the self-identification seems to me more a tribal choice than one rooted in genealogy. It so happens, of course, that it fits with the Confederate South.

During the 19th century the movement of the demographic continued into Missouri, northern Arkansas, Texas and, starting in 1889, Indian Territory, which became Oklahoma. My paternal grandfather considered himself to be of Scots-Irish descent, was a redhead - and, presumably, literally a redneck, and my paternal grandmother settled in Indian Territory in the early 1890s on Cherokee land. My maternal grandparents were also in Indian Territory in the 1890s and settled in the same county, Dewey County, sandwiched between Osage county on the west Nowata and Rogers county on the east and Tulsa county on the south. Kansas was the northern border.

Almost all of my mothers siblings settled elsewhere - several in Texas, one in California, one in Florida. Most of my father's siblings stayed closer to home, though my cousins on that side have mostly left Oklahoma. Both my mother and father were born at the tail end of large families. My mother's family was more prosperous than was my father's.  

"It is not necessary to have hope in order to persevere."