Don't worry he doesn't know what he's talking about with the US channels either. NBC, CBS, ABC, and FOX are not subscription or "basic cable" based (except the cable extensions like msnbc etc). They are ad based. They are commercial and not non profit like the BBC. PBS is also non profit, and is a PUBLIC broadcasting company, funded by about half donations/grants from individuals and companies, the rest government backed.
However, PBS doesn't own it's station affiliates. It's affiliates pay PBS to put certain broadcasting on the air and PBS acts as a body to acquire the programming and distribute it to it's affiliates. But because these stations pay PBS for the broadcasting, they for the most part can choose what they air and don't have to answer to PBS that much. Therefore the programming is part national and part local (like depending on the city local).
So really, the reason the "American Equivalent" of PBS confused people so much was because there really isn't one. PBS is the closest as far as it's public, but it doesn't have near the size or funding of the BBC or CBC, it's funded in different ways(the affiliates paying them), and they do not own their partner broadcasting stations.
edit: I wasn't completely clear on the funding so to be clear it goes.... Donations to local affiliates by business/people > affiliates pay PBS for the programming that PBS acquires (way #1 PBS gets money)> Government also funds part of it (Way #2 PBS gets money).