"I think we all know that corned beef & cabbage is Irish-American, not Old-world Irish. (That's why the people who make it sing inauthentic songs.)"

Well, I think that your first point has been proven wrong, but even if the dish is simply "Irish-American", does that make Irish-American's "inauthentic"??    Cultures develop and celebrate their heritage in many ways. Irish-American culture is different from Irish culture.

While it has not been popular in Ireland, corned beef did originate in Ireland (as discussed above). It has become "adopted" as part of the Irish-American celebration of St. Patrick's Day, so you would be wrong if you say it is "inauthentic".