Well, 1st gen chinese restaurants that serve both Americans and Chinese usually have a "separate" chinese menu.
They have standard "americanized" menu posted behind and above the counter, but they also have a paper form old-school menu all written in Chinese, and have traditional chinese dish on them. So unless you know Chinese, you can't even order them.
BTW, I've seen 1st gen Chinese restaurants with Mexican cooks. It was a very popular store among the 1st gen Chinese customers.
Heck I've even seen Japanese restaurants with Udon-serving mexican cook, and it tasted just fine.
I've had better Japanese food cooked by hispanic cooks than Korean or Chinese run stores.