Large language models (LLMs) produce stable self-reports on personality inventories, but these self-reports do not predict observed behavior. Whether this gap reflects a mismatch between LLMs and human trait constructs, or a deeper property of LLM self-report itself, has been unresolved. We constructed the first psychometric instrument whose constructs are derived bottom-up from LLM behavioral affordances via exploratory factor analysis (EFA). We administered 300 items (240 direct Likert + 60 scenario-based) spanning 12 candidate behavioral dimensions to 25 LLMs across 17 model families, each item administered 30 times. EFA yielded a 5-factor structure -- Responsiveness, Deference, Boldness, Guardedness, and Verbosity -- with excellent split-half replicability (all Tucker $φ\geq .957$) and internal consistency (all $α\geq .930$). To test predictive validity, we collected 2,500 open-ended behavioral samples rated by 151 human raters and a three-judge LLM ensemble. Human and judge ratings agreed ($\bar{r} = .51$), but neither tracked self-report: self-report--human $\bar{r} = -.01$, self-report--judge $\bar{r} = .13$, with no factor-level self-report--human CI excluding zero. On Responsiveness, self-report correlated with LLM judges ($r = .53$) but not humans ($r = .04$), even though humans and judges agreed ($r = .59$) -- indicating self-report items and LLM judges share variance that human observers do not, a confound invisible to within-ensemble reliability checks. We release the instrument as a diagnostic probe for alignment-shaped self-description and a concrete risk factor for LLM-as-judge pipelines.