Well I might be too knee-deep in academia to be a fair judge, but every university is a bunch of independent researchers of variable quality with wide latitude

Well I might be too knee-deep in academia to be a fair judge, but every university is a bunch of independent researchers of variable quality with wide latitude to pursue whatever and it seems silly to judge a university's reputation based on some individual researcher (or alumni, or whatever). I think any conflation is more the fault of media articles about the research than anything else. Yes, you write your affiliation on papers, but that does not really construe any sort of endorsement. I'm sure one can find many Stanford faculty expressing contrary viewpoints, but those are not (for whatever reason) being amplified by the media. I can put a crazy paper on the arXiV tomorrow with my affiliation and if some media report says "The University of Chicago is claiming a perpetual motion machine" or whatever, that's the media's fault for misrepresenting the situation.