I have no experience of handling a complaint like this, but surely the BBC must get a lot of vexatious and utterly nonsensical allegations through all the time. In this case, they emailed asking for more information and got no response. They called the mobile number they'd been given and it didn't connect. That must surely have given them the impression that the complainants had perhaps had a change of heart or were not serious.
I feel for the BBC senior management in all this. They seem to have got caught up in a family drama, at one level anyway.
Also, it's a bit rich for politicians to be expressing serious concern about this when there are so many ongoing sex scandals involving allegations of sexual assault and rape involving current and former members of Parliament. All a bit convenient, frankly, especially given the email making serious allegations about George Osborne last week.