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Some--not all--foreign students are of families that are based in another country and have family businesses in those countries, the incomes of which are not subject to U.S. taxes. In college (reputable public university) I knew several well-off Chinese-American students from Hong Kong and Taiwan who had come to the States in grade school, lived in expensive neighborhoods, attended private schools or top public schools, and would go back to their childhood homes during summer and winter breaks. Their parents had jobs in this country, never anything that seemed especially lucrative, and the kids didn't really talk about the influx of overseas income--they commiserated with the rest of us on a budget--but every so often, they'd show up with expensive things that their parents or grandparents bought for them that I could never ask mine to buy for me.
It was a different experience than in high school, where the Chinese-American students/Americans of Chinese descent were suburban middle class as were most of the other kids.
(Apologies for the hyphenation. I'm not sure what nationality they would consider themselves.)