If you need more proof that AI detectors fails in education, this paper makes the case so simple and clear. These "AI detectors" tools are conceptually unsound because, in real student work, there is no independent ground truth to verify whether a flag was actually correct. Even a detector with a perfect record on false positives would still fail, because the students it misses are the ones skilled enough to disguise their output. What ends up being punished is not AI use but clumsiness at hiding it. A detector's accuracy rate tells you nothing about whether any particular flag it raises is correct. Turning that rate into a probability about any one flagged case needs the base rate, which is unknowable. So a classifier deployed where ground truth is never observable cannot settle an individual case, only justify a closer look. Detectors measure something real on labelled corpora, but this paper argues the measurement cannot travel into settings where nothing confirms authorship. Even a detector with no false positives does not fix this: in the paper's hypothetical, such a tool cleared 27 papers of which 11 were entirely AI-generated.