Why would they make such distinctions? When you are talking about the difference in the "cailber" of student from any of the schools in the lower t-14, you are making distinctions between 2 LSAT points or so. Why would an employer care about that?
You're assuming that the distinctions are based on firms' perceptions of which schools are "better." As I said above, most of the distinctions are based on random preferences. Many hiring partners prefer their alma maters. Other hiring partners just want more from a particular school because they haven't been particularly successful at recruiting from that school in prior years. Yet other hiring partners have a proven track record with some schools and not with others, and prefer to take the safer bet.
You'll see these preferences flair up in various ways: NU students preferred to Cornell students at some firms, and yet other firms will take a GULC student over Cornell or NU or Duke students. Other firms simply must have that one Stanford student. If it's an east coast firm, then that means they'll have to dig deeper into SLS's class for that student than at HLS or NYU or CLS, simply because their class is so small and not so many voluntarily come out to the east coast to work.
The examples are numerous. This is what partly motivates the confidentiality behind GPA-offer statistics at various schools. Some firms have obvious favorites and would rather not expose this to either their competitors or students at other schools.