Of course they do. The aren't allowed to print anything they want. Public service is governed by state. Well at least in Sweden but the principle is the same.
No, they just calculate with increased size of the training roster.. it's not that complicated. Which is a fair presumption as that is how we've increased the predictive precision so far.
Well obviously they cannot rule out techniques no one has though of but likewise they obviously accounted for what they deemed to be within the realm of possibility
What you mentioned is assumed video and paper in question.
The main argument being that no matter our computational techniques, the diminishing returns in predictive precision is reached far sooner than we achieve general intelligence.
BBC is regulated by the government in the form of Ofcom according to:
https://www.bbc.com/aboutthebbc/governance/regulation