To touch on the US and BBC World, some viewers do get the channel, but to talk about the number of viewers because of PBS stations is a bit absurd. PBS is a large network, but each station (and in any city given the number of communities and amount of public TV volunteer donating, you may see anywhere from one to four PBS stations on your schedule at once). They're all independently programmed, and so depending on the city you might not get any BBC World.
Even in San Francisco, which is pretty heavily saturated with public media, affiliate KQED runs a 30 minute bulletin recorded at some point in the day and repeated over and over (same newsreader, same "broadcasting on PBS in America and around the globe" opener.) That's a bit of a disappointment.
Furthermore, BBC Worldwide decided to limit the amount of access to the World News by amending their contracts so that only one PBS affiliate in any region can have a license to run World News. So while KQED does run it in San Francisco, other stations nearby like KRCB or KCSM couldn't. As you could expect, this amendment tends to favour the wealthiest/largest affiliate.
To top it all off, just because it's in households doesn't often mean anyone is watching it. The PBS specialty is "programmes that no profit-seeking enterprise would afford to run," or at least that's what they tell you when they ask for funding. Most Americans associate PBS with educational content, complemented with things most wouldn't ever be bothered to see like three hour operas.