Multimodal agents increasingly choose tool calls from screenshots, documents, and webpages, where a false perceptual claim can turn hallucination from an answer-quality error into an authorization failure. We formalize this failure mode as hallucination-to-action conversion: an unsupported claim supplies the precondition for a privileged action. We propose evidence-carrying multimodal agents (ECA), which treat free-form model text as inadmissible evidence, decompose each tool call into action-critical predicates, obtain typed certificates from constrained DOM/OCR/AX verifiers, and use a deterministic gate to authorize only the privileges those certificates support. Rather than hiding perception error, ECA converts opaque model belief into auditable residuals at the verifier, schema, and implementation levels. Verifier red-teaming across 17 canonical attack categories shows that four targeted hardening steps are each necessary; after hardening, canonical gate bypass is 0/1,700 (Wilson 95% upper bound 0.22%). With content-derived certificates, ECA observes zero unsafe executions on 200 end-to-end tasks (Wilson 95% upper bound 2.67%) and 120 browser tasks (upper bound 4.3%). A HACR audit on 500 stratified task keys shows that unsupported action-critical claims reach unsafe execution for naive agents (100.0%) and prompt-only defenses (49.6%), but not for ECA. Oracle-certificate replay over 7,488 GPT-5.4 traces isolates gate correctness, while neural judge baselines still admit most unsafe actions under the same threat model. The resulting principle is simple: model language may propose tool use, but certified predicates must authorize it.