A-F school letter grade systems, currently used in 13 states across the United States (U.S.), are one popular version of the systems required by federal policy to help states define, rate, and label school quality every year. In this study, we explored the extent to which such grades assigned to schools, as based on objective measures including students' achievement test scores, may reflect school demographics and other, non-achievement-based school indicators. We found that letter grades do indeed reflect school demographics in a non-random way, thwarting the validity of the inferences to be drawn from states' A-F grade system output, which is critically more important when consequential decisions (e.g., school funding decisions, of pertinence in the state of focus in this study -- Arizona) are attached to A-F grade output. More specifically, we found that school demographic composition (e.g., race, free-and-reduced lunch [FRL] eligibility, and English language learner [ELL] status) are strongly associated with school letter grades and the combination of these factors correctly predicts the letter grades received by schools with a 75% accuracy.