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:

http://ideas.repec.org/a/ilr/articl/v55y2002i4p686-699.html

I don't have access to the paper, but from the summary I see no evidence that this measure has any empirical support.