I remember working for The Sun at the time when Rebecca (then Wade) was editor, and was arrested for assaulting her then-husband Ross Kemp. It was a story that rival newspapers and Sky alike jumped on with glee: 'hard nut editor of top tabloid beats up famous hard man husband' type thing. The same day Steve McFadden, who played Phil Mitchell, had his then-girlfriend arrested for assaulting him. It was tabloid heaven, both EastEnders Mitchell brothers 'beaten' by 'their women' on the same day, and tabloid queen Wade was in the thick of it. I recall Wade getting out of the police station and coming into The Sun newsroom (which is lined with plasma screens showing rolling Sky news, all of which were running her story) to a standing ovation from the staff. "The boss (RM) is in town", she said, "I had to give you all something to write about..." They all loved her for it.
Of all the editors and execs he employs across his media empire, I think RB has always been a favourite of his, and enjoyed a very cosy relationship with him. Saying that, Murdoch was always much more hands-on with his UK papers than US ones, I believe. When he was in town he would sit in on editorial meetings, was involved in the hiring and firing of top editorial staff at his papers - not just editors, but section editors - and often approved big stories before they ran.
So perhaps she lies somewhere between unofficial daughter/favourite, and firewall for his son, James (who certainly is the prodigal son).