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I still wouldn't conflate the two.  I know of some high reputation colleges out there that are small and are only undergraduate in focus.  

I would agree that the high research universities also tend to be good academically, especially in STEM fields.  I don't know of an exception.  It's like the AAU thing, it mostly relates to grad schools.

As I often note, we humans like rankings, I guess it saves us from having to do our "own research" (which often is silly as well).  I think a lot of it matters when one lists a school on one's resume, it either gets your foot in the door, or closes the door, or cracks the door open a bit.

Can a person get a good education at say Northwestern State?  Of course.  Or a bad one at Stanford?  Of course.  But the latter will open a lot of doors for you because more Stanford grads will be elite than grads from NWSU.

Does it matter if Stanford happened to have a fairly low research expenditure?  Not that much, in my opinion.  Some of the most renowned professors are poor teachers and vice versa.