Anecdotally it really seems like this should be true.
Cities in mostly ethnically homogeneous states tend to still have things of value that might draw people of diverse ethnic backgrounds. I'm in Nashville Tennessee and there are far more people of Asian or middle Eastern descent here in the city than there are in the surrounding rural areas, due to the universities and the job opportunities which draw people from out of state.
But Tulsa, OK vs the surrounding non-metro counties? I'm less certain without diving into the data.
The median US city size is Naperville, IL at 149,104 people.[0]
[0] https://en.wikipedia.org/wiki/List_of_United_States_cities_b...