King rarely meant you ruled a country. In English it was usually a nickname from Middle English king: someone with a lordly manner, someone cast as the "king" in a pageant or festival, or occasionally from a personal name King. Irish families sometimes translated names containing rí ("king") into King.
In North America the spelling also absorbed German König, French Roy, and other "king" cognates. That mix is why confidence is likely: the English nickname is the lead, but one Census bucket holds several stories.