The BBC has to decide if people are stupid or intelligent.
If the former, then embedded reporters will continue to be interviewed in politically correct terms by talking heads about unverified snippets from dubious sources while spilling the beans in selective fashion, and people will use the internet to find the other side of the coin.
If the latter, then it has to get out of the way and allow disparate points of view to be put by those who hold them, and their narratives aired sufficiently fully so people don't have to use the internet to make up their minds. Since some narratives are more complex and/or harder to put across, it has to jettison its specious simulacrum of a concept of "balance" - which in any case would be irrelevant. (The question of when to pull the broadcasting plug on a narrative might be settled in various ways. One would be to see when it degenerates into tedium, repetition, blatant adversariality, tendentiousness, ad hominem attacks, personality cult, etc).
Mumbling about science, rationality or the postmodern is irrelevant.
Science is no seamless tapestry - discordant theories can be found wherever you look with an unprejudiced eye, and there are also facts which require hand-waving to be performed. Science does not even apparently require logical consistency, since you cannot believe in both quantum mechanics and the theory of relativity and be correct. Neither can it explain why one atom in a lump of uranium underwent decay just now, rather than a different one.
As for rationality, if this is to mean something more than how mental processes proceed in different tribes and tribal areas, it really needs an intellectual overhaul which does not leave reason itself as the privilege of a select few tribes or as a mode of life which one tribe can seek to impose on another. In other words, as Kant saw, but more modern (quotes optional) thinkers (quotes optional) prefer not to, either we all are capable of reasoning in one and same way, or none of us are.
I suspect this premise of the debate is obscured is because it could reveal who the censors of the present really are.