The most obvious answer is that the expense of a boarding school could not be justified. Or, the mother preferred to have her daughter raised in the U.S. by the mother, personally.
Liberty High School is in no way portrayed as a school lacking in academic quality nor funding. The school is going to be a reflection of the community in whatever country it is located. Liberty is located in an upper-middle class community. And like most American communities, athletic prowess is almost as valuable in social currency as how wealthy your parents are or what possessions you may have.
In other settings, the social currency may be for what company your parents work, to what political party they belong, or which religion or sect they subscribe. People are people. And, they will form a social hierarchy of inclusion and exclusion based on whatever external factors they deem desirable. I have yet to see a culture that doesn’t. Brown-nosing comes in all colors, shapes, and sizes. Even in private schools.
The antagonist character, Bryce, is portrayed as coming from a very affluent family. His families wealthy is displayed as more of a contributing factor to his preferential treatment than his athletic prowess.
In this way, Liberty is no more “scruffy” or “gruff” than any other American high school portrayed in mainstream media. By all accounts, the academic expectations of the high school is just as high for jock as it is for nerd. And, most of the main characters display more than adequate intelligence.
I live in a similar type of neighborhood in the American central Southwest. More than half of the adults in my neighborhood are either first generation Americans or permanent resident aliens. To encounter a child in school with a foreign accent is neither unusual nor a cause to request an explanation. The same could be said of these children. Why didn’t there parents put them in a boarding school back in their home countries? Maybe, because their parents want their company and the opportunity for the parents to raise their children themselves.
The flip-side of that is that I know people who have decided to send their children to boarding school. Some of the boarding schools have been in their home countries. Some of the boarding schools have been here in the U.S. Some of the boarding schools have not only been here in the U.S., but have also taught using the structure and curriculum of the schools in their home country. Mostly, of the parents who have sent their children to boarding school that I know personally, the parents remain in their home countries and send their children abroad to the U.S., Canada, Australia, Israel, England, Switzerland, etc.