Not to go totally academic here but that's a structuralist viewpoint, in my opinion. And structuralists are pretty cool - not a bad viewpoint at all. Personally, I really love the work of folks like Ian Hodder who has been looking at things from a (his term) post-processualist viewpoint (http://en.wikipedia.org/wiki/Ian_Hodder). This implies that normal is often an artifact of analysis, not a feature of culture. There are whole books on this, so hard to summarize, but perceived cultural boundaries are most commonly actually gradations of different attributes of humanity, and historians and anthropologists often draw these arbitrary lines around clusters of these attributes and call it "normal" (aka "normal American"). That often isn't how the emic (internal to culture) folks view it at all..
Example, I feel generally more culturally connected to people from Vancouver than people from Maine, even though being a Californian, my country is often viewed as my cultural anchor from the etic (outsider) perspective.
I'm not saying you're wrong, I'm saying there are other ways to look at this, than "normal" being the definer or creator of culture.