Recently, she was tasked with a company exercise of gathering and presenting information about each persons personality type. On recieving John's data, she announced to the office that he shares the same personality type as serial killers.
This is utterly unacceptable. There is normally a very strong code of ethics attached to doing any sort of personality profiling. She is either unqualified or in a major breach of ethics. If she was tasked with the information, she should be expected to act with the same level of professionalism. If she was not specifically responsible, those responsible should be aware of her comment(s). This is something that should be brought to the attention of HR and/or the individual responsible for the program. (I may be able to give more information if you knew which system they used.)
If she does do things like this, I recommend he approach her privately first and express it... chances are she'll wave it off and do it again. Then do it in public the next time she does, and rebuke her hard. I've heard variations on "This time I do have something to say. As I told you before, I don't appreciate your comments and believe them to be unprofessional/unkind/uncalled for/etc." I've also heard people say that the other person "is misunderstanding the difference between introverts and extroverts - introverts take time to think before they talk, to avoid making comments that hurt others", but that was more when people crossed the line.