LLM-based multi-agent systems promise effective collaborative reasoning, but communication may amplify local errors into collective risks. Existing evaluations emphasize final outcomes, leaving the reliability and propagation dynamics of distributed information aggregation unclear. We introduce Hi-Agreement, a controlled evaluation framework that strictly pairs all-honest collaboration with controlled deception by a key evidence holder and analyzes the aggregation process through multi-stage voting, testimony adoption, and evidence-root lineage propagation. Using 120 five-agent object-movement environments where partial observations jointly determine a unique endpoint, we evaluate 3 homogeneous LLM-based multi-agent systems. Across these paired conditions, aggregate truth recovery falls from 72.50% to 14.17%, with significant declines for every system. Process tracing and exit ablations show that a single false testimony is adopted more readily than truthful testimony, propagates to higher orders, and persists through honest agents after the deceiver exits. Observers without first-hand evidence suppress incorrect consensus but do not improve truth recovery. Together, these findings reveal both the fragility of distributed fact recovery and its underlying mechanism: false evidence gains collective influence through its adoption and continued propagation by other agents after entering communication.

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