When High Accuracy Misleads: Unequal False-Positive Risk and Bias in AI-Text Detection

AI-text detectors are increasingly studied for educational assessment. Of their two errors, one falls on the student: a false positive, where authentic work is marked as AI-generated. Detectors are judged by overall accuracy, which counts the mistakes but not who they fall on. We examine this with PROBE (Protocol for Robustness and Bias Evaluation), holding out one of 15 topics at a time from 44,861 student assignments and scoring only the topic withheld. Every verdict is joined to the grade an independent rater gave the same work. False-positive rates on authentic writing then rise at every step, from 0.92\% at grade 1 to 5.18\% at grade 6, a 5.6-fold difference. The most highly graded writing carries the greatest risk of being wrongly flagged. Within grade bands, flagged work carries denser formal discourse markers than passed work, consistent with the detector responding to formal register rather than grade itself, though our design does not establish it. These detectors look strong by conventional measures, averaging 98.11\% and 98.18\% on the unseen topic. Yet an authorship-blind control counting only word frequencies averages 98.88\%, so accuracy alone does not establish authorship detection. High aggregate accuracy can therefore coexist with unequal false-positive risk, and evaluation for educational use should report how errors are distributed across students, not accuracy alone. Corpus, code and per-fold results: \url{https://anonymous.4open.science/r/GRADE-Study-B584}.