Large language models (LLMs) are used worldwide, yet exhibit Western cultural tendencies. Many countries are now building ``regional'' or ``sovereign'' LLMs, but it remains unclear whether they reflect local values and practices or merely speak local languages. Using India as a case study, we evaluate six Indic and six global LLMs on two dimensions -- values and practices -- grounded in nationally representative surveys and community-sourced QA datasets. Across tasks, Indic models do not align better with Indian norms than global models; in fact, a U.S. respondent is a closer proxy for Indian values than any Indic model. We further run a user study with 115 Indian users and find that writing suggestions from both global and Indic LLMs introduce Westernized or exoticized writing. Prompting and regional fine-tuning fail to recover alignment and can even degrade existing knowledge. We attribute this to scarce culturally grounded data, especially for pretraining. We position cultural evaluation as a first-class requirement alongside multilingual benchmarks and offer a reusable, community-grounded methodology. We call for native, community-authored corpora and thickxwide evaluations to build truly sovereign LLMs.