The rapid development of Large Language Models (LLMs) has transformed fake news detection and fact-checking tasks from simple classification to complex reasoning. However, evaluation frameworks have not kept pace. Current benchmarks are static, making them vulnerable to benchmark data contamination (BDC) and ineffective at assessing reasoning under temporal uncertainty. To address this, we introduce LiveFact a continuously updated benchmark that simulates the real-world "fog of war" in misinformation detection. LiveFact uses dynamic, temporal evidence sets to evaluate models on their ability to reason with evolving, incomplete information rather than on memorized knowledge. We propose a dual-mode evaluation: Classification Mode for final verification and Inference Mode for evidence-based reasoning, along with a component to monitor BDC explicitly. Tests with 22 LLMs show that open-source Mixture-of-Experts models, such as Qwen3-235B-A22B, now match or outperform proprietary state-of-the-art systems. More importantly, our analysis finds a significant "reasoning gap." Capable models exhibit epistemic humility by recognizing unverifiable claims in early data slices-an aspect traditional static benchmarks overlook. LiveFact sets a sustainable standard for evaluating robust, temporally aware AI verification.