From the immigrant perspective that was true for many, coming from another country where any status in the US is better. They may be privileged from the perspective of others who couldn't make it out, but from the US perspective it's something different.
There is a pretty famous story from Saturday Night Live. The characters of the "two Wild and Crazy Guys" were based on an individual Steve Martin met in a bar in New York. He was an immigrant from a country in Eastern Europe and, delightfully inebriated and happy, was crowing about his new life in America. Among the things he mentioned (paraphrasing from memory of Martin describing the anecdote) "In my home country, I am doctor. Now, I sell washing machines. Is much better!"
