Matching the wavefield is not matching the CPML solver

Learned wave models are generally judged on pressure snapshots and receiver data, and a close match is often taken as evidence that the network learned the simulator. We show that this does not hold for acoustic wave simulation with convolutional perfectly matched layers (CPML), where pressure is only part of the solver state and the absorbing layer stores memory variables that affect later updates. A surrogate can match the observed pressure field while still failing the hidden state, continuation, or derivative needed to replace that solver. We show this by comparing against the declared CPML solver at five levels, wave kinematics, receiver data, pressure and memory state, continuation, and the full waveform inversion (FWI) derivative. The clearest failure is a trained Fourier neural operator (FNO) with snapshot error around $0.13\%$ and receiver error around $0.10\%$, yet completing its missing memory leaves a recurrence residual around $0.03$, above both a loose $10^{-2}$ diagnostic and the $10^{-4}$ solver threshold. The completed state does not satisfy the declared recurrence even though the pressure evidence looks strong. The same gap reaches FWI because inversion uses the solver derivative, not only the matched pressure field. On 100 local FWI targets whose receivers sit in the CPML layer, the FNO Jacobian increases the exact CPML objective on 11 of them. The same test is harmful on 56 targets for a receiver-only stencil with no memory, and on 0 for exact CPML and for a full-state readout with the correct tangent. So pressure agreement is not enough evidence to replace the solver, restart from it, or take an FWI step with its derivative.