If you torture the data long enough, it will confess to anything. ~Ronald Coase
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At most LACs that statement would be called a non-sequitur.
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Resisting the urge to reciprocate by commenting on the logical reasoning skills of LA majors. 
I suspect that If @brantly had phrased the subject line, “What defines a liberal arts college?”, it would have burned itself out after ten posts; we think we know what an LAC is. It’s the word, “university” that is the confounding element. I think there’s a big difference between universities that have a strong undergraduate focus on the liberal arts and those that do not. What say, you?
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Most of the criteria are meaningless:
Caltech is smaller than nearly all the well-known LACs, but it is a research university.
None of the schools (except one) with the ten lowest student-to-faculty ratios are LACs:
35 Best Student-Faculty College Ratios for 2022 – Colleges of Distinction.
This is far from universal. Many research universities offer well-rounded general education and a few LACs are highly specialized.
But at least five of them would fit my definition of a “liberal arts university”. Thanks for getting us back to answering the OP’s question. 
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A qualifying word in each of these statements makes them far from meaningless and pretty accurate. 1. tend, 2. generally, 3. tend
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It’s meaningless and inaccurate in the sense that these criteria can’t be used to define/delineate a LAC (let alone a “liberal arts university”).
But they’re also research universities.
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Are the terms mutually exclusive?
I’m not sure. I’m as confounded as you. People have been treating a liberal arts college as something that’s distinct from a research university. But is a liberal arts “university” completely separate from a liberal arts “college” and is not so distinct?
Colloquialisms are words and expressions that become commonplace within a specific language, geographic region, or historical era. IMO, LAC has become this for the most part.
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This thread is lengthy and murky, but I will take a stab at it. If we are truly talking about universities, not liberal arts colleges, then the dividing line between university and college is clear. A university offers graduate programs (like Colgate University), while a college does not (like Dartmouth College) 
A liberal arts university would focus mostly on the traditional liberal arts, while also offering graduate programs. I would call Princeton (as a poster did above) a liberal arts university. But a Penn or Columbia, which have schools of Business, Law, Nursing, Social Work, etc., the percentage of students studying the liberal arts is probably less than half. That doesn’t exclude them having excellent liberal arts colleges and programs inside the university, but the term “liberal arts university” wouldn’t include them in my book. YMMV.
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There’s no problem if a school calls itself (or others call it) an LAC. The problem arises when the claim is made that there’s certain uniqueness, beyond without having graduate students (which isn’t always true), about being an LAC. The often-cited characteristic, “small class size”, for example, isn’t a function of being an LAC. It has more to do with the size of the school, the student-faculty ratio, etc.
Still not sure why that’s a problem. Just because there are exceptional cases doesn’t mean the generalization is without its uses. You’re trying to create a corollary to your argument that there is no such thing as the liberal arts because schools teach computer science. No one else sees that as a problem that requires dumping the baby out with the bath water.
I get it. It is just a marketing construct. Every large state flagship offers as many liberal arts courses as you want. Leaving aside size, fashionableness etc… Just because there is a business school attached it doesn’t mean that you can’t get a pure liberal arts education
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Other than LACs being typically small and usually without graduate students, I’m not sure there’re other defining characteristics. To me, being liberal arts or not isn’t a good way to classify colleges or universities. It’s much better to classify them by the breadth of their general educational or core curricula and the depth of their major-specific requirements. Amherst, for example, is a universally recognized LAC with an open curriculum. Presumably (someone with better knowledge about Amherst please correct me if I’m wrong), a student there could theoretically graduate with a very narrow focus on a specific subject. So, did s/he graduate with a (supposedly broad) liberal arts education?
Computer science is another complication. Some required courses (e.g. theories, algorithms) in CS fit the traditional liberal arts definition, but many others (e.g. programming classes and the like) are clearly more vocational in nature.
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Math is, of course, the traditional domain of the LACs, and computer science has been incorporated into the traditional Liberal Arts approach since the mid 1980’s at the latest.
But in the condescending views of some, isn’t “undergraduate focus” just another name for handholding students who lack logical reasoning skills to gain entrance to the superior research universities?
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Empirically the first kid who goes to a top LAC probably starts at the 90th or 85th percentile in the class (in terms of rank) in a typical year at our school. The top kids all go to non-LACs.
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