Large language models (LLMs) are widely used as cross-lingual knowledge interfaces. However, culturally grounded questions often reflect globally dominant narratives rather than local contexts. We study this failure mode as \textit{global narrative dominance} in Bangla, a low-resource cultural context. We introduce \texttt{CulturalNB}, a dataset of 717 manually curated Bengali cultural instances with parallel Bangla--English question--answer pairs and supporting evidence, metadata, and sociocultural annotations. Using question-only and evidence-based prompting, we evaluate nine state-of-the-art LLMs with human and two independent LLM judges across metrics for cross-lingual consistency, language anchoring, global substitution, institutional bias, and epistemic perspective coverage. Results show that questions asked in English systematically increase global substitution and institutional framing while reducing local perspective coverage. Local evidence improves factual consistency and perspective coverage, but does not eliminate language-induced epistemic shifts. These findings suggest that cultural failures in LLMs are not only missing-knowledge errors but also failures of grounding and narrative prioritization.