I realize it may be too late now to back to the OP, but I wanted to add something.
I think the truth is inbetween the idea that Americans have a severely abbreviated culture and Hyphenated-Americans are Really Really Hyphenated People.
America was colonised in waves, and those waves often consisted of people from distinct linguistic and cultural groups, usually settling in similar areas to each other. The parents bring the culture with them, from their homelands, but the children born there...well, they exist in a different geographical, legal, political and economic climate to the one their parents did, alongside other emerging or distinct foreign cultures as well.
Thus you have a case of divergent cultural evolution. Much like the way Canadian French is different from Modern French, but related historically and linguistically, you have an Irish Tradition with an offshoot - the American-Irish tradition, and the Irish one. Conditioned by outside factors and the course of history, there is inevitably going to be a major difference in how those traditions are percieved and what kind of behaviour they result in.
The only reason Irish Irishness is considered more legitimate than American Irishness is because the former controls the state of Ireland, and thus the percieved homeland of Irish Tradition by both sides.
Thanks Cain. Your five concise paragraphs spared me an hour of typing, getting logged out and losing an hour's worth of typing.