Sadly (and stupidly) our system lets them do this for summer courses.
That does not mean that I have to re-teach everything I've taught so far this week -- in my office -- so that someone who can't get registered (or contact me) in a timely manner can pass the exam the class will be taking over the weekend.
Also, I will not set this student up for failure from the start - nor will I waste the first two class meetings (almost the equivalent of two FULL semester weeks) because our system permits this. Summer semesters are compact enough without blowing off two class meetings.