Having studied in the sciences at both a competitive private and a mid level public university, I can say that it is absolutely true. The only classes I took that were taught by TAs were labs; all of the lectures and seminars were taught by professors.
Many of the course offerings were the same (specifically at the lower levels), but the private school offered more upper level ones, courses the public one didn't offer because none of the faculty studied the topic (also because fewer faculty meant fewer people to split the lower level courses). Also, since when were course requirements the metric by which a program's value measured?
I wasn't aware that nuanced "teaching ability" had to be quantifiable to be brought up here, nor was I aware that I used the words "teaching ability". The professors at the top universities know their fields better; they are able to talk about the questions, controversies, and emerging topics in a way that professors elsewhere can't, and this absolutely comes through in the classroom (again, personal experience).
Lastly, as you acknowledged, the faculty are there for research, which is part of the educational experience. Any scientist at a university is going to be having undergrads work for them, research experience at a top university is generally going to be more valuable than at a lesser one.
Sorry that I didn't just look college rankings when I made my post