Normal people think of the primary purpose of a university as educating undergraduates. If the only education going on in a research institute is apprenticeship as a researcher, possibly with some directly relevant technical courses this is so far from most people’s experience of a university as to be a different thing. Professional academics may disagree but if an institution goes from encompassing a broad section of society to a narrow one, from educating and doing research to doing research and education only as necessary to that and from providing a space for maturation and relaxation before adult life to being a professional workplace that’s a pretty drastic change.
A research university is a lot closer to a non research university than it is to a research institute.
Medical school faculty, especially in soft-money positions, might never set foot in a classroom. Some of them will even have labs that are almost entirely postdocs and technicians. This doesn't seem wildly different from a research institute to me. If anything, the funding is probably less stable too, since you're on your own.
A research university is a lot closer to a non research university than it is to a research institute.