Do universities hire graduates from lesser universities
People are occasionally hired by far more prestigious universities than the ones they studied at. For example, there's a tenured professor in the Princeton math department (unambiguously among the top 5 departments in the U.S.) who received his Ph.D. in 1999 from Kansas State (which wouldn't necessarily make the top 75). Where your degree is from is a negligible factor in hiring decisions compared with how outstanding your research is.
On the other hand, research excellence is highly correlated with which doctoral program you attend. The top programs tend to get the students with the most talent, determination, and preparation, and they usually provide the most support for these students to succeed. Of course this is just a statistical assertion, not an absolute law. However, in mathematics in the U.S., the number of students graduating each year from rank 50-75 universities whose job applications are as impressive in research as those of the average top-5 graduate is tiny. If you're hiring based on research promise, then even the most unbiased search should lead to hiring mainly people from higher-end schools. Of course there's presumably some prejudice as well, but I don't think it's a substantial factor at research universities. (I have no first-hand experience with hiring at teaching-oriented schools. In particular, I don't know how overrepresented graduates of prestigious universities are or which factors are responsible for it.)
The top ranked doctoral programs get the cream of each year's incoming graduate application pool because they can offer access to the top professors, top research libraries, and have tons of money to spend on tuition waivers, stipends, summer research money, etc. They can effectively outbid other programs and choose the people who seem to have the most promise (or are advantaged in having Famous People write for them, etc. etc.).
Graduate students at top ranked programs don't have to spend as much time doing non-research activities such as teaching and waitressing to pay the bills as they're getting most of their living expenses covered. They instead can focus on their research and publications, resulting in a flush CV by the time they graduate.
This leads grant agencies and hiring departments to assume that the graduating students at the top ranked programs are indeed the best of the best. They certainly have the imprimatur of the Best Programs® and Famous People® are writing them letters of support.
This is almost certainly a flawed assumption, but when faced with 200 grant or job applications, it's a shortcut many search committees make. Ideally they should just look at the candidate's qualifications without considering the school or the Famous People® who wrote for them.
But even if we redacted program names in applications, the very fact that having gone to a top-ranked place gives people a huge material difference/advantage in resources available while they are in the program, and this is evident in their CVs which are long with lots of publications and talks in the Right Places®.
In a totally fair world, we'd do what google does and throw away (or at the very least redact) CVs and letters and instead interview people one by one. But try to convince a provost and a search committee to go along with that. It would take too long and cost too much.
Interestingly, as fewer and fewer people get jobs straight out of graduate school and everyone now has to have a post-doc or visiting position, this has served as a slightly equalizing factor as hiring schools can look at performance there as a better indication of inherent ability.
Note 1: People can and do move from lower ranked to higher ranked schools, but usually they don't do it in their first job. Rather, from a low-ranked they get hired at a mid-ranked school, then through publishing and publishing and publishing, they get hired away into a top-ranked (perhaps going through one or two job hops along the way).
Note 2: Top ranked universities (as well as everyone else) have overproduced so many PhDs in pretty much every field that there is market saturation. Even graduates at top-ranked programs are having trouble finding jobs -- even as adjuncts and NTT faculty. In a true market economy, the suppliers would be forced to lower production in the face of oversupply, but academia is not a market economy and having doctoral students is seen as a source of prestige for both faculty and institutions alike. Unless we can increase demand (by forcing schools to hire TT faculty instead of contingents, or other means) or reduce supply, we're all screwed but the folks graduating from mid- and lower-tier schools are screwed the most.
Here's a numerical perspective on this. Let's take the position that students graduating from highly-ranked schools have competitive advantage against other students (i.e. they are "better", and will generally be hired when their applications are compared with students of less prestigious schools). Now, consider how many positions are available at each level:
Undergraduate: Typically, a college will have hundreds if not thousands of students in each year, of varying majors. In my major (math), let's say 5% of the class has it. At my school there were 1000 students graduating, so let's say 50 math majors (actually, it was more like 80).
Graduate: Typically, a graduate school department will have tens of students per year. A small number of tens; at my undergraduate institution (Chicago), the corresponding graduate school has about 100 total students, for about 20 per year. So, with similar figures at other schools, only 0.4 of math majors can go to graduate school. Fortunately, not everyone wants to.
Post-doctoral: Most math departments only have a handful of postdoc positions; let's say 10 (which is actually on the high end). So only 0.5 of graduating students can get postdocs. Of course, there are teaching jobs available at schools that don't produce PhDs, but those are "lesser universities".
Tenure-track: In any year, any department might have three of these. Or one, or none. That means that 0.3 of postdocs will go on to a more permanent position.
At each stage the number of people accepted to the next level is a small fraction of the total number of applicants, and so the schools can pick and choose whom they take; of course, they will take the "best" applicants, which (according to my conventions) will generally come from the highly-ranked universities. The alumni of just the top 10 universities are sufficient to fill all positions at all universities that are at all desirable (to researchers, that is).