[Kojak]

Is that distinction relevant enough to the general public though? They are all still major programmes made for the BBC. 

The BBC has nobody else to blame but itself for the mess it has made of this situation.

I think the general public would see a bigger distinction between sports and entertainment programming than they would between News and Current Affairs and Sports.
The reality is that the BBC Sport brand is extensively used during news programming in a way that entertainment brands are not and also many of those used on final score and match of the day work within the news and current affairs departments the rest of the week.

It's still not news, though. Well, sports news, I suppose, but not news news. Anyway, it's not as if Gary Lineker pops up during the week with the BBC Sport updates on the news channel. He only really does Match of the Day and the odd big football match. He's no more a part of the rank-and-file BBC Sport department than you or I.