@bay, what do you define as “amenities”?
I know of at least one elite private (and there probably are others) which doesn’t have a climbing wall or what some people on here call amenities (the student union is also kind of run-down). They still charge the same high list price as everyone else, though. Probably because they can.
Plus, there are plenty of publics that cost less than list price at a private.
Note that the bare-bones type of school UCB is referring to in other countries is invariably a public.