These horses have similar markings as the wild Kiger Mustangs in Oregon.

Kiger Mustangs are a distinct, protected population of wild, free-roaming horses found in the Steens Mountain region of southeastern Oregon. They are descendants of early Spanish horses and are known for their dun-colored markings.

Rewilded from a 12 cohort population which was already descended from interbreeding with domesticated Horses so this is at best a back-fill and probably we can't get fully back to the root.

They're truly wild within the limits of "true"