This kind of thing exists on a lesser scale even for kids who want to graduate one year early (so ~21). Even on this forum, you can search and see how forum regulars advise those students to take that extra year and research or take grad classes rather than graduate early.
In addition, there are some graduate programs that are not open to people without "life" or career experience. If you want to be a school principal, for example, you need to teach for 5 or 10 years first. And any program for school administration that accepts you without that kind of teaching experience is setting you up for a near impossible job hunt afterwards. As a teacher, I would not work under a principal who had never taught. Imagine this girl had majored in secondary education -- she would be teaching students older than herself! The thought of her trying to control a classroom or break up a fight. She would be having the same difficulties getting a job. Saying this, I'm not aware of the specifics of clinical psychology, but I don't think there is a clear cut yes or no age answer for every graduate program. I mean, if she were a math major, there wouldn't even be an issue of her age in my opinion.