Sorry, but the academic paper you linked to is complete garbage. To quote
"Lacking a direct measure of aptitude, we link people to the mean combined SAT scores of their college and then divide them into six groups: those from colleges with SAT scores in the top five percentiles, the next 10, the next 15, the next 20, the next 25, and the bottom 25 percentiles. The SAT cut-points are constant over time so that aptitude is defined in absolute terms. The aptitude groups are finer at the top of the distribution because previous research suggests that the top quartile accounts disproportionately for the decline in teacher aptitude."
Whoever wrote this should lose their tenure immediately.
Caroline Hoxby, who wrote that, voluntarily left her position at Harvard to gain her current position at Stanford. If you haven't heard of her before, you should read more National Bureau of Economic Research working papers.
But what specifically are you disagreeing with in the paragraph you kindly quoted?
I'm balking at the idea that the mean combined SAT of the college a teacher attended is predictive of their teaching quality, both currently and longitudinally.
I'm not saying that it's impossible, but basing an entire paper on this premise without any supporting evidence is completely ridiculous. So far as I've seen there is zero evidence that this is true.
After some Googling, it seems that this measure of teacher quality is attributed to:
"Lacking a direct measure of aptitude, we link people to the mean combined SAT scores of their college and then divide them into six groups: those from colleges with SAT scores in the top five percentiles, the next 10, the next 15, the next 20, the next 25, and the bottom 25 percentiles. The SAT cut-points are constant over time so that aptitude is defined in absolute terms. The aptitude groups are finer at the top of the distribution because previous research suggests that the top quartile accounts disproportionately for the decline in teacher aptitude."
Whoever wrote this should lose their tenure immediately.