Although you seem to have accepted that the testimony provided by your sister’s accuser is indeed “evidence” you seem to think that a prosecution cannot reasonably succeed without the support provided by other evidence, simon. This is simply not the case. Many cases, particularly those of a less serious nature which are handled in Magistrates’ courts, often revolve around one person’s word against another. The CPS will assess the evidence provided by their witness and decide if it is likely to stand scrutiny in court. (Note this does not necessarily mean they are certain of a conviction, but that there is a reasonable prospect of success). If it will, they authorise a prosecution. It is then for the CPS prosecutor to present the evidence to the court and for the court to determine a verdict.
Your sister's case sounds as if it is a summary matter that will only be heard by Magistrates. If it is they have no powers to dismiss the case before hearing the evidence formally (and as I have pointed out earlier, they will have no idea what evidence will be presented anyway). The CPS can, of course, withdraw the matter at any time, but that is not the same as the case being dismissed by the court. The only powers the Magistrates have in these circumstances is to convict or acquit but they cannot do this before hearing the evidence. If the defence lawyer believes the prosecution have not made out their case he can ask the court to rule that there is “no case to answer”. If this is agreed the defendant will not have to make out a defence. But once again this cannot be done before the prosecution evidence is formally heard in court.
It’s really quite straightforward: once the CPS has decided to prosecute only courts decide whether the prosecution evidence is good enough to support a conviction or whether the defendant is acquitted. Nobody else can.