Immersive storytelling increasingly relies on distributed architectures to enable collaborative co-creation across remote participants, but network impairments such as delay and burst latency can introduce inconsistencies in shared object states, avatar gestures, and spatial audio cues that disrupt narrative coherence. While prior work has examined the perceptual impact of de-synchronization, existing approaches do not formally characterize the structural conditions under which such inconsistencies break narrative coherence and, consequently, narrative integrity. In this paper, we introduce Narrative Interaction Coherence (NIC), a system-level metric that captures causal event ordering violations, temporal misalignment, and state divergence in distributed immersive environments. We develop a simulation framework for collaborative storytelling under controlled network impairments and compare latency-based and QoE-inspired adaptation strategies with a coherence-aware approach. Results show that coherence-aware adaptation substantially reduces narrative break events and incoherence duration, maintaining high coherence even under adverse conditions. These findings highlight the importance of explicitly modeling structural narrative coherence as a design objective in immersive media systems and provide a foundation for future validation in real multi-user XR environments.