PBS, like all distributors, licenses content from producers of content--sometimes PBS is the producer, often it is not--for distribution inside a defined territory.
For example, Doctor Who, Red Dwarf, Downton Abbey, and Are You Being Served are all British TV shows licensed by PBS for distribution in the US. PBS can't stream them worldwide same as the BBC can't show some of the content it distributes outside of the United Kingdom.
Or do you mean as an American in the US?
The BBC use the same provider as a number of Vegas gambling services, and they're very effective because Vegas is willing to spend lots of money on forensic work.
This is why new Sesame Street episodes are now on HBO and not PBS
It's kind of backwards to be doing business this way. There are plenty of Youtube channels that have a wider reach than many TV shows with millions of subscribers and views per video. The trick is simply to ensure you have copyright for all content that you create plus a world wide distribution license for any third party content embedded in that (e.g. background music). This is basically how Netflix works these days and one of the reasons they are mopping up the media market that is still focused on creating and selling content for individual TV channels.
It absolutely isn't.