Large language models (LLMs) have raised hopes for automated end-to-end fact-checking, but prior studies report mixed results. As mainstream chatbots increasingly ship with reasoning capabilities and web search tools -- and millions of users already rely on them for verification -- rigorous evaluation is urgent. We evaluate 15 recent LLMs from OpenAI, Google, Meta, and DeepSeek on more than 6,000 claims fact-checked by PolitiFact, comparing standard models with reasoning- and web-search variants. Standard models perform poorly, reasoning offers minimal benefits, and web search provides only moderate gains, despite fact-checks being available on the web. In contrast, a curated RAG system using PolitiFact summaries improved macro F1 by 233% on average across model variants. These findings suggest that giving models access to curated high-quality context is a promising path for automated fact-checking.