Why do prep school application forms ask you to state which other schools you are applying to?
It really is none of their business!
In the area we live the prep schools are oversubscribed (so we are led to believe) so by offering places to those they judge as the most suitable candidates (by 4+ assessment) they have nothing to lose, as there will also be a waiting list to fill declined offers.
Are they hoping that the prospective pupil has not applied anywhere else and, therefore, thinks that their school is the best? Enlighten me!