I agree with Hime, it depends.
Having said that.... I lean toward siding with the universities. If a particular student can't pass the introductory courses, how will they pass upper-division courses? If you look at math, well, I know math profs who teach "general math" courses (i.e. a notch below "college algebra" or "precalculus") where students can't successfully learn to apply the pythagorean theorem or calculate percentages of a number--things that, arguably, they should have learned long before they got out of high school. You can argue till the cows come home about whose "fault" this is, but I personally feel people like that shouldn't be enrolled at a university. (Ditto for those who can't read and understand a book, or write a coherent paragraph.)
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