Despite remarkable advancements in Multimodal Large Language Models (MLLMs), a fundamental question remains: are MLLMs robust to contradicting modalities? To rigorously study this, we introduce MMA-Bench comprising videos and tasks that probe a model's reliance on specific modalities. Using black-box and white-box interpretability techniques, we provide a critical analysis of the brittleness of both open- and closed-sourced MLLMs. We show that current MLLMs struggle under misaligned audio-visual pairs and simple misleading text, thereby lacking robust multi-modal reasoning. Building on these findings, we propose a modality alignment tuning strategy to teach the model when to prioritize, leverage, or ignore specific modality cues. Through extensive experiments and analysis, we show that our alignment tuning yields demonstrably stronger multimodal grounding. This work provides both interpretability tools and a clear path toward developing MLLMs with intrinsically reliable cross-modal reasoning. Code and dataset will be publicly available.