I think the reverse is actually true, at least among all my wide-eyed friends.
When White or Black Americans see someone who looks, well Oriental (Chinese, Japanese, Korean, Vietnamese, Thai), they immediately think CHINESE. They do not think Asian.
Asian includes India, Pakistan and various other countries where the people do not resemble Chinese.
It seems to me that this is psychologically another way to hide. Chinese businesses, except the restaurants tend to be very bland. The restaurants (especially the all-you-can-eat buffets) with the red and gold trim and the huge characters that only Chinese can read (at least around here) are the only exceptions, and some restaurants are a lot less ostentatious.