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1) Your point about responding students about Princeton surveys as well does not refute anything about the response rate of Berkeley grads.
Berkeley has 50+ people at Harvard Law School which indicates 15-16 people getting in per year, yet the admit rates according to the career center varies greatly per year from 3 to 12 according to the surveys. Since Berkeley is a big public school that offers very little help to applicants there is probably a lesser chance of students responding to surveys at Berkeley versus a smaller, more intimate private school.
In addition, for the 15% that get accepted from Princeton, who among them actually goes to UCSF? Probably much less than half. These are people that are headed for Hopkins, Harvard, etc. as well. Adcoms are well aware of crossadmit rates and adjust their number of acceptances accordingly.
Those that get into UCSF from Harvard with 3.7's are probably in general as smart as those that got into UCSF from Berkeley with 3.9's. Did they work as hard? Maybe, maybe not (Berkeley has grade inflation in many majors too). Its not perfect, but its still a very fair system.
If you were going to get into Harvard Medical School from Princeton you would probably still get into it by going to Berkeley. You would have to work harder if you majored in the sciences at Berkeley, and you would get no help from the university in terms of advising, so it is in ways more difficult. However at the same time, your peer group is much dumber, so it will be easier to make better grades while on a curve in many cases versus Harvard/Princeton.
Lets not draw spurious relationships from incomplete facts. Berkeley students does about as well as you would expect from the quality of the admits
You're confusing PR with reputation. It's not the same thing. Bad PR is for example publishing the best combination of SAT scores as opposed to the best score component from different sittings, which schools like USC do.
PR relates to administrative efforts in presenting their institution under the best light, while reputation tends to be based on peer assessment and actual achievements (like discovering 17 elements on the table of elements and having 18 bona fide Nobels.)
You mentioned Emory and Rice as having smaller brand names, yet those schools are elevated to Berkeley's level by the USNWR. Berkeley doesn't care much about its USNWR standing (except for Haas, which makes an effort to for instance make sure that its students report their job offers and so forth), while schools like Washington U make it a driving institutional mission. Haas used to be towards the bottom of the teens not too long ago as an MBA program, it has climbed to the bottom of the top 10 by and large, due in good part to good PR which has allowed it to be ranked close to its true standing.