Culture is not some independant thing, it is composed of the collective characteristics of a group of people. If a stereotype has some basis in the culture, it therefore follows that there must be some basis for that in the people that compose the culture. This doesn't mean it's always the case, but based on the preceeding statement, it doesn't seem logical to say that they are completely unfounded, either.

It sounds like the study asked different people how they rated themselves, which also introduces a huge degree of error. Suppose modesty or arrogance or some other such characteristic were a significant part of a culture- the effect this would have on how members of that culture rated themselves and others should be obvious.