I believe the previous comment is correct. I don’t think professors can save a spot of “pre” register students for their courses. They CAN approve a student to enroll in a course that is showing up as full. I bet she’ll get the class she needs during the first week back.
I’m sorry your daughter put you through this. She could have gone to an internet cafe and taken care of this herself and saved you from worrying.
I’m with Robert. I’ve never heard of someone at UVa failing to graduate on time because of a full class.