Social media platforms have become primary channels for health information in the Global South. Using gomutra (cow urine) discourse on YouTube in India as a case study, we present a post-facto Large Language Model (LLM)-assisted discourse analysis of 30 multilingual transcripts showing that promotional content blends sacred traditional language with pseudo-scientific claims in ways that sophisticated debunking content itself mirrors, creating a rhetorical register that LLMs, trained predominantly on Western corpora, are systematically ill-equipped to analyse. Varying prompt tone across three LLMs (GPT-4o, Gemini 2.5 Pro, DeepSeek-V3.1), we find that culturally embedded health misinformation does not look like ordinary misinformation, and this cultural obfuscation extends to gendered rhetoric and prompt design, compounding analytical unreliability. Our findings argue that cultural competency in LLM-assisted discourse analysis cannot be retrofitted through prompt engineering alone.