This does not alarm me as I have noticed that it is very common for Koreans and other non-Japanese asians to open restaurants that serve Japanese food (teriyaki, yakisoba, etc.) They even decorate the restaurants with Japanese art, posters, maps of Japan, etc. It's merely a matter of marketing. Americans like and are used to Japanese food more than Korean food.
Similarly, it does not seem unreasonable to conclude that an Arab would make more money serving Mexican food that Arab food. I wasn't clear from your post if the host you mention was an owner. Even if he wasn't, I have eaten at ethnic restaurants where not all the servers were of matching ethnicity. BTW, how did you know that he was "Middle Eastern"?
The ones you have to watch are the Muslims who open an "American" restaurant in a foreign city. Avoid it.
He did not speak very good English, and he did not speak Spanish enough to be able to converse with the authentic Mexicans who were working there. I believe that particular Mexican restaurant went out of business.
As for his Middle Eastern-ness, I believe I relied on hubby's knowledge rather than my own. But I couldn't tell you what it was about the guy. It's been too long.