In a room full of experiences like above, no one is counting the "depth" of cultural connection, nor would it be appropriate to say so. You wouldn't say "how Mexican are you?" And suppose that a 2 or 3 generation Mexican American (born US, never returned to Mexico significantly) was not still importantly connected to their heritage.

No one from America thinks they are citizens from anywhere else (unless they have the passport). But as a nation of immigration, heritage is of social interest, and all take pride in what parts they are made from. They don't think they are literally Italian or similar.