They do not as all their slots had already been taken and it was not they who had made any mistake
Foundation program is a separate program run under the University of London for all its colleges. They do not necessarily fall under administrative control of the individual colleges
As mentioned in my initial summary a complaint was indeed made, but since the school in question has nothing to do with whatever did happen, the people at the foundation program apologized and said congratulated her for having managed a slot at Kings College. No further option to complain remains. Either sue them or just shut up!