In general, the reliability coefficient doesn't take into account extra distributional knowledge. If you knew that scores were power-law distributed in the population but the test error were normally distributed, for example, then you would want to calculate the posterior the long way: with the population data as your prior distribution and the the measurement distribution as your likelihood ratio distribution, and the posterior is the renormalized product of the two. I don't think that using a linear correction based on the reliability coefficient would get that right, but I haven't worked it out to show the difference.

That makes sense, but I think the SAT is constructed like IQ tests to be normally rather than power-law distributed, so in this case we get away with a linear correlation like reliability.