Why does the American Samoa and Puerto Rico get olympic teams and they don't say anything about the U.S. Virgin Islands? Also, why can't all three just be part of the U.S. team?
The IOC is the body that basically decides, for the purposes of the Olympics, who and who doesn't qualify for the purposes of being a country. Puerto Rico, Guam, American Samoa and the Virgin Islands(
they are at Rio too) in the eyes of the IOC, despite legally belonging to the US are deemed sufficiently sovereign enough to technically count as if they were representing themselves.
Puerto Rico, Guam, US Virgin Islands and American Samoa, while noted above as belonging to the US, are culturally different, and with the exception of military and some foreign policy decisions are completely autonomous. They have their own laws, they can elect their own governments, set their own procedures for legal matters ect...all without US approval. Adding to this that the cultures in these areas are deemed unique enough to separate them from the traditional 50 states demographics.
For example, the US and the Virgin Islands both boycotted the 1988 games in Moscow, but Puerto Rico still sent its own team to compete.
Granted, just because the IOC says something is a country doesn't mean it actually is. They're a private organization after all.