Looked him up too and said his paternal grandfather was Irish. Found this - Anthony Rudolph Oaxaca Quinn was born in Chihuahua, Mexico to Francisco Quinn of Irish-Mexican descent and Manuella Oaxaca of Mexican and Cherokee ancestry. His father was fighting in the Mexican Revolution with Pancho Villa's forces at the time of his birth until the family fled to El Paso, Texas to escape federal troops.
My mother was born in 1915 in southern Oklahoma and my dad 1910 in eastern Oklahoma. Maybe my parents and your dad crossed paths or they all saw an Anthony Quinn movie.