To add one thing here: the professor in question is at a school in the top 20 worldwide. Almost every applicant had a basically perfect GPA from high school, but some of them had SAT scores that were 70th percentile or below. The SAT seems to "scale up" to that market much better than GPA as a predictor.
Right; GPA is a coarse representation of performance on coursework. A 4.0 at Stuy with coursework on real analysis and organic chemistry means something very different than a 4.0 at a struggling inner city public school where the hardest math class is Algebra 2.
My point is more that universities can (and do!) create a different representation of coursework performance that accounts for rigor. But a university that eliminates the SAT is also likely intentionally making that representation less predictive of undergraduate performance to allow weighing of things more than preparedness/quality as indicated by grades.
What makes SATs so important is that you get a very limited preparedness signal from kids with 4.0 at the crappy school; combining test scores with GPA allows for a selective school to get a much more meaningful signal for quality/preparedness.
My motivation here is to push back against the scores alone are enough idea, though it's an understandable reaction to the people who by all appearances think quality/academic preparedness should be a secondary concern in admissions.