I would add that perhaps many Chinese restaurants do not want too many non-Chinese customers. Especially for immigrants, restaurant life is often about ambience, social contacts, and feeling you have a space to call your own.  A restaurant cannot be all things to all people and the #1 best way of judging a restaurant is to look at its customers.  The "beef with broccoli" menu will attract a certain kind of American customer, but without breaking down the sense of segregation and the basic Chineseness of the place.

That said, there is also the fear that the American customers will order from the secret menu and then not like the chicken feet, etc. and give a bad report to their friends.

他大概就是说中美口味不同, 其实我虽然压根不知道到美国中餐馆有不同菜单这回事,但即使有这回事, 基本上就是针对不同口味的人群推出不同的菜嘛, 免得因为口味不同而说菜不好吃而破坏了名声.

当然Cownen说的中式餐厅不想要太多非华人顾客也有点道理, 就像在美国感觉很多华人物业主都不愿意把房子租给非华人, 主要是很多美国华人在和美国人交流上还是存在一定的障碍, 包括文化 语言 等等.

PS 原博客有过百人对此事的讨论, 如果懂英语的可以去看看. 有兴趣的人也可以到我博客留意和阅读其他文章.