[qwerty123]

In the case of the likes of Lord Sugar or Mark Gatiss, The Apprentice is made by Fremantle and MGM TV so he's not actually employed by the BBC per se, Gatiss created Sherlock through Hartswood Films which again is an indie.

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.
You also wouldn’t expect to see someone move from a drama or reality programme presenting the news but multiple people at the BBC move between News and Sport frequently, especially in the regions, again suggesting that BBC Sport falls under BBC News.