The caveat does say only South or Southern but Saudi is just south but in Arab.
1933, from Sa'ud, family name of the rulers of Nejd from 18c. and of the kingdom of Saudi Arabia since 1932. The name is from Arabic sa'd "good fortune, happiness." With common Semitic national designation suffix -i.
There is a set of communities south west of Detroit, collectively known as 'Down River,' but you shouldn't date guys from there. "Down River Man...." news headlines are Michigan's version of, "Florida Man..."