Stereotypes are based on fact, hence their origin. The fact that not 100% apply to their fact-based origin is enough for stupid people to dismiss them.
You don't have a stereotype that Chinese are great basketball players because they are not. You have a stereotype that blacks are great basketball players because they make excellent basketball players. This does not mean, however, that all blacks are great basketball players.
Naturally, if a stereotype deals too much truth and is not PC, then it will be dismissed.
