It seems to me the BBC are damned however they treat the incident.
Carol Thatcher was stupid to have used the word and was unfortunate that some prat leaked it to the press. But that's the risk of being a 'celebrity'.
It should have been sorted out among the people having the conversation and no one else.
Any bugger with an ounce of sense and in the public eye should have been aware that ANY phrase, word or sentence uttered by them will always be under scrutiny. Posters on here are also aware that the word is out of order when referring to another person, that's the rules, like it or lump it we have to live with it.