I also can't think of a single "ethnic" food available in our area that we don't eat. Like someone said, I don't even think of many of them as "ethnic", since they are so commonplace. We love Chinese, Japanese, Thai, Vietnamese, Mexican and Greek food, and also eat Indian, Moroccan, German, Italian, and Korean on occasion. I had some great co-workers who would bring in specialties from various African countries, as well, those were always delicious! Unfortunately, I know of no restaurants in our area that serve that type of food.
Funny, I'm half Italian and half German, but we eat less of those foods than many others. I never really thought about that until just now.
ETA: oops forgot to answer this part. I don't really care about the ethnicity of the people running an ethnic restaurant, as long as the food is good. In our area, most of the Mexican food is pretty bad, the only good places happen to be run by Mexicans. I've never been to a Greek place not run by Greeks, but some of our favorite Asian places are run by people from other Asian countries.