Cultural representation in Large Language Model (LLM) outputs has primarily been evaluated through the proxies of cultural diversity and factual accuracy. However, a crucial gap remains in assessing cultural alignment: the degree to which generated content mirrors how native populations perceive and prioritize their own cultural facets. In this paper, we introduce a human-centered framework to evaluate the alignment of LLM generations with local expectations. First, we establish a human-derived ground-truth baseline of importance vectors, called Cultural Importance Vectors based on an induced set of culturally significant facets from open-ended survey responses collected across nine countries. Next, we introduce a method to compute model-derived Cultural Representation Vectors of an LLM based on a syntactically diversified prompt-set and apply it to three frontier LLMs (Gemini 2.5 Pro, GPT-4o, and Claude 3.5 Haiku). Our investigation of the alignment between the human-derived Cultural Importance and model-derived Cultural Representations reveals a Western-centric calibration for some of the models where alignment decreases as a country's cultural distance from the US increases. Furthermore, we identify highly correlated, systemic error signatures ($ρ> 0.97$) across all models, which over-index on some cultural markers while neglecting the deep-seated social and value-based priorities of users. Our approach moves beyond simple diversity metrics toward evaluating the fidelity of AI-generated content in authentically capturing the nuanced hierarchies of global cultures.