What you are claiming is that the US has no identity, no culture, nothing and that it is defined by any foreigner coming here and claiming their previous culture is ours.
No. What I am claiming is that American identity is flexible enough that it doesn't require--and, indeed, has NEVER required--people to abandon their roots abroad, be it food, music, art, or the like. What I am claiming is that American culture is strong enough that it is not threatened by a beauty pageant contestant performing a Bollywood dance.