It is commonly perceived that online fake news and reliable news exhibit stark differences in writing styles, such as the use of sensationalist versus objective language. However, we emphasize that style-related features can also be exploited for style-based attacks. Notably, the rise of powerful Large Language Models (LLMs) has enabled malicious users to mimic the style of trustworthy news outlets at minimal cost. Our analysis reveals that LLM-camouflaged fake news content leads to substantial performance degradation of state-of-the-art text-based detectors (up to 38% decrease in F1 Score), posing a significant challenge for automated detection in online ecosystems. To address this, we introduce SheepDog, a style-agnostic fake news detector robust to news writing styles. SheepDog achieves this adaptability through LLM-empowered news reframing, which customizes each article to match different writing styles using style-oriented reframing prompts. By employing style-agnostic training, SheepDog enhances its resilience to stylistic variations by maximizing prediction consistency across these diverse reframings. Furthermore, SheepDog extracts content-focused veracity attributions from LLMs, where the news content is evaluated against a set of fact-checking rationales. These attributions provide supplementary information and potential interpretability that assist veracity prediction. On three benchmark datasets, empirical results show that SheepDog consistently yields significant improvements over competitive baselines and enhances robustness against LLM-empowered style attacks.