Large language models (LLMs) are increasingly used for qualitative data analysis (QDA), yet their outputs often miss the depth and nuance of human analysis. We argue this gap reflects a missing credibility practice from human QDA: peer debriefing, in which an analyst seeks feedback from a disinterested peer and uses it to refine their coding. To bring this practice into LLM-assisted QDA, we propose Agent-as-Peer-Debriefer, a multi-agent QDA framework that builds peer debriefing into key coding steps. In our framework, a Hierarchical Coding Agent follows the standard QDA process to generate codes, sub-themes, and themes, along with self-explanations and reflection memos. It then shares these outputs with three Peer-Debriefing Agents, each applying a distinct analytical perspective (Theory-Driven, Data-Driven, or Applied) and refining the codes by keeping, renaming, reassigning, merging, or splitting them. These perspectives are drawn from established human QDA practices that generalize across domains and datasets. To evaluate the framework, we test it on three datasets across two domains with three LLMs, measuring semantic similarity to human-annotated codes. Across all settings, perspective-based, peer-debriefing refinement aligns more closely with human codes than a single-LLM baseline, and an ablation further shows the gain is not merely from additional refinement. The three perspectives also produce distinct trade-offs, showing that the choice of perspective is a meaningful and controllable design decision. More broadly, these findings suggest that simulating peer debriefing with explicit perspectives is a promising route to more credible LLM-assisted QDA.