Answer:
In the practice of law, "Right" isn't really the issue. In the situation you refer to, the question is, "Did the prosecution believe that (1) a crime was committed and (2) that sufficient evidence exists and can be presented to the jury that will convince them beyond a reasonable doubt that the accused committed the crime?".
The lack of a rape kit may complicate the procesuction's case somewhat, but it's not at all a requirement. The defense will of course bring this up in trial.