I think there is no doubt that Harvard has an outstanding math department, and I agree that many prospective grad students will be aware of Harvard without being familiar with any rankings. However, there is a difference between viewing Harvard as "one of the best schools" (similarly to how one...
This is utter nonsense. There are plenty of phenomenal mathematicians at less prestigious schools, and "best" is often simply a matter of taste. How does one compare, for example, a leading algebraic geometer with a leading model theorist?
The "common knowledge" that there is a "highest tier"...