It's obvious who is intelligent and motivated to work for their grades and who is not - you can see it in choice of major (some are easier than others) and in calibre of work, especially when students collaborate on a project. If someone has a famous surname, drives an expensive car, lives in an apartment or house bought by dad off campus, and isn't shy about the fact they pay someone to write their essays you can be pretty sure they don't belong in, for instance, Princeton. Lots of factors give hints.
I agree though, that you can be both really rich and also really intelligent, and some legacy admissions would have got into the university they attend even without the connections. Their monied parents or grandparents normally wouldn't have come from landed wealth they've been sitting on for centuries as might be the case in other societies. I don't know anyone who is really rich who doesn't work extremely hard for their money and isn't really, really intelligent, often in a multitude of different ways.
The correlation between being skint and being highly intelligent in an Ivy League setting is far closer.