Sure, maybe you can make a model that outputs Harvard or Princeton's results, but how do you explain the difference between Harvard and Princeton?

Dunno. I've already pointed out the quasi-Simpsons Paradox effect that could produce a lot of different shapes even while SAT score increases always help. Maybe Princeton favors musicians or something. If the only reason to look into the question is your incredulity and interest in the unlikely possibility that increase in SAT score actually hurts some applicants, I don't care nearly enough to do more than speculate.

By the way, the paper you cite is published at a journal with a data access provision.

I have citations in my DNB FAQ on how such provisions are honored mostly in the breach... I wonder what the odds that you could get the data and that it would be complete and useful.