It is nuts. Radio is incredibly hung up on language. When Andy and I did that show briefly on Leith FM, we got a proper bollocking because I used a non-radio edit of a Pink song at one stage. Full apologies after the song, etc, etc - song pulled as soon as the word was uttered. Gladly, nobody was listening, as there were no complaints.

I fully expect the show would have been pulled if there was a complaint as radio stations can actually lose their license for stuff like that, if it's repeatedly done.
The case above, though, is totally mental - pretty indicative of the BBC's utter knee-jerk overreaction to most things. Mental.
PS - WRT the library thing - the Pink song in question was one I brought in, plus I'd imagine the Beeb local station library might not have a 1930s song in it, so it would be something the DJ would have brought in himself.