1. US is an independent country, it is not the age of thirteen colonies. 宗主国 is absolutely a wrong description
2. US are pound of themselves, US above all rest of the world.
3. i see quite the opposite: the major intake of UK university are (of course UK local student, and then a big proportion is from her former colonies in Asia and Africa; it is indeed quite rare to see a significant portion of US student in any non-US university..)