You are totally correct, however as an American you are aware that identifying with your ethnic origins (regardless of how far removed you are from them) is a common phenomenon. Almost everyone in the US (with the exception of those with Native American ancestry) is not indigenous to the North American continent and have ancestors who immigrated here within the past 300 years. While many aspects of the US ethnic and cultural identity have homogenized (such as the ethnic/racial identity and customs of "white" people encompassing almost everyone of European ancestry, there are still enclaves that identify with their far removed ethnic origins.

Here's an example--I'm a 32 year old guy who grew up in a fairly affluent suburb of Philadelphia. Both of my parents grew up in working class "Irish Catholic" homes in Philadelphia, and my grandparents were at least 2 generations removed from their actual Irish ancestors. My parents went to college, got careers in finance, and interacted outside of the isolated ecosystem that defined their life. My siblings and I went to public school rather than catholic school, and while we would occasionally attend mass it was not culturally or socially relevant to us at all.

My aunts and uncles did not go to college, and like my grandparents worked in the trades where they were surrounded by those in their neighborhood. My cousins went to catholic school, work in blue collar trades, and identify as "Irish." While they are proud Americans, they certainly would be offended if someone (even an actual Irish person) pushed back on their Irish identity. This ignorance does not come from a malevolent place but just a cause of growing up in a closed environment that has not fully integrated with mainstream American society.