STAGE: Diagnosing Semantic Transfer at Grounded Execution in Embodied Agents

Embodied language grounding requires more than identifying the referent of an instruction: recovered semantics must also control the action an agent exposes. We study this missing link as a semantic-action gap, where instruction semantics are recoverable but weakly expressed in native continuous actions. We introduce SAT-Bench, a fixed-observation counterfactual benchmark that holds the visual scene and agent state fixed while changing only instruction semantics. On LIBERO target-name and pixel-grounded relation swaps, target recovery reaches 100.0% and 95.8%, whereas OpenVLA action sensitivity remains only 6.8% and 7.7%. The gap persists across 1,000 additional compositional and temporal/procedural counterfactuals, with overall action sensitivity of 6.1%. Hidden-state, threshold-free, cross-policy, and rollout diagnostics further support this semantic-action transfer failure. We introduce VISA, a lightweight execution-time interface that converts recovered semantics into ALLOW, DEFER, target-consistency, and verified-selection decisions. VISA reduces invalid-instruction blind execution from 92.7% to 2.8% while preserving 94.0% of normal commands, and verified selection further improves target-consistent action exposure without updating the underlying policy. Overall, embodied language evaluation should measure semantic-action transfer, not semantic parsing alone.