Well if you watch the 1st 2 minutes of the show, Stanley Johnson knighthood is down as one of the topics for discussion, i.e. The BBC knew the topic would be discussed and was possible someone would bring up the wife beater allegations. And therefore yes its almost certain a lawyer did tell her exactly what to say if someone brought up those wife beating allegations.
Charlotte Wahl never made a complaint at the time, it was only mentioned much much later to a journalist who was doing a biographer of SJ. Therefore to avoid being sued, BBC lawyer probably thought it wise to clarify what was in the public domain, which was that it had been alleged and there was a qualified acknowledgment from SJ's friend that it had happened but as a one off, not a regular occurrence as CW had alleged.
The statement FB was made to say was very clumsily put together, but its a bit harsh blaming her for it, she almost certainly didn't draft the words.