Frontier LLMs perform well in Western contexts, but remain poorly tested on underrepresented cultures such as those in Southeast Asia (SEA). Existing NLI benchmarks are largely Western-centric, translation-derived, or monolingual, limiting their ability to measure culturally grounded reasoning. We introduce SEA-NLI, a native, culturally grounded NLI benchmark covering eight SEA countries in English and native regional languages, verified by native speakers. Across 17 encoder and decoder models, we observe a low performance from all models, especially for knowledge-intensive categories such as Languages and Science and Technology. Our analysis shows that failure cases mainly stem from missing SEA cultural knowledge: SEA-adapted models and culture-aware prompting improve performance, while CoT prompting offers limited gains.