I have no doubt that the Sunday Times would have investigated to establish at least whether their claims had some basis in fact – the risks would be too great to publish elsewise. It can't be difficult to establish the facts in the Botswana allegations – if she was found guilty in a court of law, that record would be available. The question ought then to have arisen – when she was appointed – whether she disclosed her criminal record. If not, she's guilty of fraud and should be summarily dismissed. If she did, other (political) questions arise as to her suitability for the appointment, but the fault there would lay with whomever did the appointing.
On the alcohol claims – given that the ST is in possession of her medical records, one can again assume that such claims are based on evidence. If I was the parent of the teenage liver donor, I'd be outraged at this waste of my son's organs, and would be calling publicly for tighter control of the organ transplant process.
As it stands, when I heard she'd originally been given a liver transplant, I tore up my organ donor card and rescinded my “living will” and made it known publicly why I was doing so.