Large language models (LLMs) give stable answers to personality questionnaires, yet these self-reports fail to predict how the models behave. Is this gap an artifact of forcing human trait categories onto LLMs, or something deeper about LLM self-report? To find out, we built the first psychometric instrument whose dimensions are derived from LLM behavior rather than human psychology. Administering 300 items (240 Likert + 60 scenario) to 25 LLMs across 17 model families, 30 times each, exploratory factor analysis revealed five reliable, replicable factors: Responsiveness, Deference, Boldness, Guardedness, and Verbosity (all Tucker $φ\geq .957$, all $α\geq .930$). We collected 2,500 open-ended samples and had them rated by 151 humans and a three-judge LLM ensemble. Humans and judges agreed ($\bar{r} = .51$), but self-report predicted neither the ratings nor objective text measures computed from them: the gap persists even for constructs native to LLMs, where a human-mismatch explanation no longer applies. The exception is Verbosity, whose self-report reaches 74% of the criterion-reliability ceiling against human ratings, but does not track raw output length. On Responsiveness, self-report tracked LLM judges ($r = .53$) but not humans ($r = .04$), even though humans and judges otherwise agreed ($r = .59$). This pattern formally rejects any single latent construct driving all three measurements ($p = .007$). Self-report items and LLM judges share a source of variance that human observers do not, and controlling for measurable surface features (length, formatting, enthusiasm markers) does not remove it. This confound is invisible to the within-ensemble reliability checks used to validate LLM judges, and it poses a concrete risk for the LLM-as-judge pipelines now central to model evaluation. We release the instrument as a diagnostic probe for alignment-shaped self-description.

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