Not only would it be like a one in a 6 billon chance that she would be randomly assigned to the person she was obsessed with finding, she's also clearly mentally ill. So the odds are beyond unrealistic AND there's a specific reason not to give her the benefit of the doubt.
The therapist can't be the child abuser she's hunting.
Which retroactively ruins the whole play. This kind of story only works if the two characters gradually learn to understand each other, and Jane can't understand the therapist if she's convinced he's another person.