Correlation =/= causation, for a variety of reasons. Here are some confounding variables that may explain why people who go to top/elite colleges are also overrepresented at top/elite law schools:
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Elite university students may be more likely to want to go to professional school in general, because they are more exposed to the careers (and people in them) that require professional school. Most people have heard of lawyers, but that is different from having a parent or a family friend who is a lawyer.
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Elite universities are expensive. Elite law schools are also expensive. The students who go to elite universities are wealthier than the students who go to lesser-known public universities and smaller private schools, and thus are more able to afford a top law school. So the kids who go to the lesser known schools may be either less likely to apply anyway OR may be less likely to matriculate if they get in because they can’t pay without going into debt.
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By dint of being, on average, wealthier and more connected, elite university students may be more likely to do the kind of internships that make them more attractive to law schools and to know people who can give them good recommendations into law school.
Those are just three - there might be some other ones that I haven’t thought of.
It is not rare for people from lesser-known colleges and universities to go to top law schools. They are certainly less represented than top schools, and I’m not saying that the education and training at a top undergrad has nothing to do with it. It matters, but not as much as people think it does.