Good Prediction, Wrong Latent Order: A Reporting-Kernel Misspecification Counterexample for Simulator-Based System Identification

When dynamical models are fitted to delayed reports, underestimating the reporting delay can make the unaccounted delay appear as an additional latent timescale. We demonstrate this in a controlled epidemic-surveillance simulator where the true admissions-to-death response has one exponential timescale and deaths have a mean reporting delay of 7 days. Validation selects one timescale under the matched assumption, but fixing the mean at 3, 4, or 5 days selects two in all 60 configurations while error over three entirely held-out weekly-death trajectories remains below 0.9%. An idealized transfer calculation attributes this to compensation between reporting and latent dynamics. The pattern is asymmetric: a fixed 11-day assumption retains one timescale but raises error to 1.66% to 2.22%. Thus accurate held-out prediction does not certify latent order; comparison across plausible, prespecified reporting-delay settings can flag observation-model compensation before learned structure is interpreted mechanistically.