What options do rejected applicants have if mistakenly told they were admitted to a program?

I was reading up the Reddit page here, which described a case of admissions error, in which:

1. 
   

   The person obtained an acceptance for a PhD program in writing.

   
   


2. 
   

   The person personally called the university and confirmed acceptance of the program

   
   


3. 
   

   The university then said that they had made a mistake, cancelling the acceptance.

   
   

What would be some things that the person can take, and if some of these actions required specific conditions, what would be the conditions be?

For the purposes of answering this question, we will assume that there is no stipend involved, and the acceptance was confirmed by the departmental admissions staff.