Adapting cultural values in Large Language Models (LLMs) presents significant challenges, particularly due to biases and limited training data. Prior work primarily aligns LLMs with different cultural values using World Values Survey (WVS) data. However, it remains unclear whether this approach effectively captures cultural nuances or produces distinct cultural representations for various downstream tasks. In this paper, we systematically investigate WVS-based training for cultural value adaptation and find that relying solely on survey data can homogenize cultural norms and interfere with factual knowledge. To investigate these issues, we augment WVS with encyclopedic and scenario-based cultural narratives from Wikipedia and NormAd. While these narratives may have variable effects on downstream tasks, they consistently improve cultural distinctiveness than survey data alone. Our work highlights the inherent complexity of aligning cultural values with the goal of guiding task-specific behavior. We release our code at https://github.com/faridlazuarda/from-surveys-to-narratives.