American culture has no fine dining of its own.

This is a stupid position to take. American cuisine, like American literature or film or music, does derive quite a bit from the fact that almost all Americans are descendants of immigrants (rather than the native population that was largely decimated into very small populations through war, genocide, disease, and conquest), but plenty is still invented here by people who were born here. Yes, almost all of us speak a European language, but Europe doesn't get to claim our literature or poetry. Similarly, our music uses scales and temperament and instruments developed in, like Austria and Italy, but American music is still its own thing.