I don't know about BBC or NPR, but VOA and Radio Free Asia are much more borderline. A valid argument can be made that they are not really independent of US government.
https://en.wikipedia.org/wiki/Smith%E2%80%93Mundt_Act
There was a Smith-Mundt Modernization Act of 2012, but I can't tell if that had any meaningful impact on whether the VOA can advertise to Americans.
(I know Facebook is used worldwide. Can the entities which purchase ads say that their ads must never be shown to people of certain nationalities? Would that suffice in the face of a Federal law?)
As for BBC vs NPR, the BBC is funded by what is essentially a tax, the license fee, whereas NPR is mostly funded through fees, grants, sponsorships, and contributions; in 2012, 10.9% of its funding came from Federal sources.