I have to respectfully disagree with the content (but not necessarily the conclusion) of your post, Chris. I say this for several reasons:
1. We do not know her mother's profession. Perhaps her mother is a psychologist, psychiatrist, or speech-language pathologist. Then her mother would be perfectly qualified to make a diagnosis. Who knows our new friend Anne better than those she lives with? Perhaps her mother is a special education teacher, or otherwise works with children who have autism spectrum disorders quite freqently. Then I would say her mother also would know enough about Asperger syndrome and about her daughter as a person to make that judgement.
2. Even when diagnosed by a professional, the tests are very subjective. For children, actually, the process tends to involve simply observation and having the parents answer a questionnaire. Asperger's (and autism) are not hard-and-fast diagnoses, and the label that is put upon you tends to reflect the experience of the professional who is doing the labeling. People tend to have a bias towards their own hypotheses. One professional might diagnose someone with Asperger's, while another professional, while looking at the same individual, and the same set of evidence (behavior, self-report, family-report), might choose the label of borderline personality disorder, based on having more experience with that and having the symptoms often look fairly similar.
3. Along the lines of bias, a person also has a tendency to put forward the symptoms of what they believe they have and "conveniently" (but not always intentionally) forget other symptoms. For example, if you actually had asperger syndrome, but were seeing a psychologist because you were feeling depressed, and you did not previously have a lablel, you would probably talk about the times when your emotions were low, when you couldn't re-regulate to feeling okay again, what makes you upset, how long you are sad. You might forget to mention that you have sensory issues--that loud noises hurt your ears, that you only eat certain textured foods, etc. This is quite feasible with adolescents with asperger syndrome, as it is often not diagnosed until mid-teens, often when something is going wrong (and they are becoming depressed or anxious--this happens quite frequently in teens with asperger's).
4. The attitude reflected in what you have said seems to hold the label of Asperger syndrome as something of a status symbol. I don't know if this is intentional or not, but that is the underlying message that I get from reading it. In actuality, the purpose of having any sort of label is to receive the services you need in order to live a fulfilling life, whatever that may be: occupational therapy, social skills counseling, psychological/psychiatric therapy (yes, there is a stigma there, but many/most people with and without AS could really benefit from this), disabilities services, etc, etc.
Based on what I have said, I would say that Anne should list her status as whatever she feels closest to what actually describes her. I assume this is why you included the "unsure" option in that mix. Only Anne can really decide how she wants to portray herself, both on this site and in real life. There are advantages and disadvantages to having a label; on this site, one of the advantages seems to be that it is a status symbol, and that some may take you "more seriously"--When I post on this forum, I often wonder if I will be taken seriously, or if people will ask "what does she know, she doesn't REALLY have AS," even when I have indeed have a doctor say that I do (but then I chose not to go for the full eval because I did not think that I wanted any of the services that would be offered, or possibly forced upon me).