I'm in the US and I'm not paying anything to see this article. So what's the logic for letting me see it for free but not letting someone in the UK see it?
My opinion is that without the £3.5 billion a year that comes from the UK license fee, and the infrastructure and resources that the Beeb has built up over the years due to that income (plus what they also get from general taxation), they would be hard pressed to make these kinds of programs.
As a license is required for pretty much everyone who wants to watch any live TV in the UK, its always worth the trouble for any license fee payer to ask them to justify why BBC content is (apparently) available to non UK based viewers but not to those in the UK . http://www.bbc.co.uk/complaints/complain-online/
It appears you're lumping the "BBC" in as one entity, when it is in fact many entities. World Service and the Domestic BBC are separate entities - and World Service's profits go back to the domestic BBC so more revenue beyond your license fee is available.
What are these general taxation revenues you are talking about? As to why the content isn't available, you didn't pay for it, so what's the problem? I'm willing to bet it's not available because of some rights restriction.
"We're sorry but this site is not accessible from the UK as it is part of our international service and is not funded by the licence fee."
I am also concerned that the BBC is blocking British users!