The rise of misinformation underscores the need for scalable and reliable fact-checking solutions. Large language models (LLMs) hold promise in automating fact verification, yet their effectiveness across global contexts remains uncertain. We systematically evaluate nine established LLMs across multiple categories (open/closed-source, multiple sizes, diverse architectures, reasoning-based) using 5,000 claims previously assessed by 174 professional fact-checking organizations across 47 languages. Our methodology tests model generalizability on claims postdating training cutoffs and four prompting strategies mirroring both citizen and professional fact-checker interactions, with over 240,000 human annotations as ground truth. Findings reveal a concerning pattern resembling the Dunning-Kruger effect: smaller, accessible models show high confidence despite lower accuracy, while larger models demonstrate higher accuracy but lower confidence. This risks systemic bias in information verification, as resource-constrained organizations typically use smaller models. Performance gaps are most pronounced for non-English languages and claims originating from the Global South, threatening to widen existing information inequalities. These results establish a multilingual benchmark for future research and provide an evidence base for policy aimed at ensuring equitable access to trustworthy, AI-assisted fact-checking.