Beyond Plausible Prediction: Safety Sufficiency in Web World Models

Web world models increasingly predict the consequences of candidate actions before agents act, yet a plausible predicted future does not necessarily support the correct safety decision. In a matched human evaluation of 3,000 predictions from ten frozen open models, 86.1% are judged semantically plausible. However, several models exhibit highly asymmetric authorisation behaviour, combining low false-safe execution with poor recall of clarifiable ASK cases and a strong preference for BLOCK. This motivates safety sufficiency: whether a predictive interface preserves and exposes the policy-decisive information required to distinguish actions that may be EXECUTED, require clarification through ASK, or should be BLOCKED. We introduce SafeWebWorld, a benchmark for evaluating safety sufficiency across five web-safety domains through action-conditioned futures, policy-decisive evidence, and policy-conditioned decisions. Under a controlled Security-Aligned Supervised Fine-Tuning protocol, evidence preservation can improve substantially while authorisation-sensitive decisions deteriorate. To determine whether this deterioration reflects loss of authorisation-sensitive score structure or a failure of the decision readout, we introduce Latent Authorisation Recovery (LAR). Frozen-score recalibration reveals substantial but backbone-dependent recovery, while paired recovery provides only a modest additional gain. Yet within-family and matched-authorisation evaluations remain poor, showing that aggregate recoverability does not imply robust fine-grained authorisation behaviour. Overall, plausible prediction, evidence preservation, and aggregate recovery are each insufficient on their own to establish robust authorisation.