If you exclude Western Europeans from your "immigrants" statement, which is what the parent comment was clearly implying, it's not even close to true.
Diversity is also language, culture, language, identity etc.
The slightly racist assumption in America is that if I as a white Norwegian settle in America I contribute less to diversity than a black American who has lived his whole life in America.
In America diversity is all about what you see on the outside.
The differences between accepted social behaviour in Britain, Spain and Poland are significant too.
Sure, if you came from Saudi, you'll feel more out of place. But it's not trivial.