Say you wrote a good thesis on some discovery you made in physics.
If it was a mediocre discovery, nothing special, are you more likely to get awarded the PhD at a 'not very good' university than at a top class university like Cambridge?
The quality of a thesis depends on several factors, the PhD student, the advisor and the work environment of the department where they work. th ePhD student should do the work and come up with own ideas and drive the work forward, more so towards the end than early on. the advisor, in most cases have established the basic research questions for the project in which the student works. The advisor also has a responsibility to facilitate understanding of the scientific method, ethics and plain knowledge to the student through the advisory role. The department may or may not have resources to provide a good work environment which includes size of collaborating research groups, lab space etc.
From this view it may be likely that a top tier university has more funding, has attracted "better" (however you wish to define that) scientists and lastly may attract better students (at least from the perspective of competitive application processes). It is, however, clear that these ingredients may not necessarily lead to success but it would not be a wide stretch of the imagination to say that basic conditions may be better and that this is reflected in the theses produced.
The bottom line, however, is that a good research environment is more likely to produce better work than just top tier ranking. In some cases bad luck may lead to poorer output, for example if the ice samples from Antarctica on which you completely rely for your work melt in a freezer accident. The question that remains is to what extent good research environments are determined by tier ranking.