Large language models are widely used to simulate survey respondents, yet their outputs are homogeneous and unfaithful to real inter-group differences, and whether this reflects what a model knows or uses has remained untested. Using representational similarity analysis against Pew American Trends Panel ground truth, we score demographic read-out locations in Mistral-7B and intervene causally across six attribute types. The internal geometry is faithful: attention-head read-outs dominate the standard residual read-out, reaching selection-corrected $ρ$ up to 0.63 -- about 70% of the measurement-reliability ceiling -- and one head, L11 H16, is significantly faithful across all six types, though race-based types stay weak and prompt-fragile, replicating in a second model family. Yet causal use does not track fidelity: the clearest causal pathway ($p=0.002$) sits in one of the least faithful types, the most faithful type shows no correction-surviving effect, and full identity swaps in the prompt move predictions by under 2% of their error. A 128-dimensional probe on that head lands 21-31% closer to survey truth than the model's answers, yet recovers almost none of the per-question group ordering. Readable, faithfully arranged, and causally used are three dissociable properties of the same model; treating them as one claim is what keeps the "can LLMs simulate populations" debate unresolved.

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