This is generally speaking an excellent comment about which I agree more or less completely, but your final statement doesn't really tie it all together and instead is itself an example of a fallacious statement. Even if it is true that there is a lot of diversity between nations with a majority Muslim population, it does not necessarily follow that there are not certain opinions and responses to stimuli that we might expect within populations which ostensibly adhere to the same religion. Indeed, much of modern social science (Weber, Durkheim) was founded on articulating the differences between predominately Catholic and Protestant countries, including the now famous "Protestant work ethic."

Of course, at the time I'm sure it was politically incorrect to say that "Catholics are lazy," and even now that would be an astonishingly rude over-simplification -- nonetheless it is possible to make generalizations on the basis of aggregated data that are generally correct.

To chose a somewhat less politically sensitive example, if one were to look cross culturally at fundamentalists within monotheistic traditions, I suspect you would find that they support wife-beating at a much higher average than the general population -- of course, this is a much more politically correct way of going about things, insofar as you don't disturb things too much by pointing out the problems in people who are, generally speaking, quite far away from you -- nonetheless, we are able to make these sorts of generalizations accurately and there is no reason why we can not also do so for the Muslim world.