Propagation-based fake news detectors primarily extract structural patterns from news propagation trees via graph neural networks (GNNs), which are crucial for trustworthy information access on social platforms. However, these systems remain vulnerable to adversarial message injection, increasingly enabled by large language models (LLMs). Such attacks pollute both semantic and structural signals, causing GNN-based aggregators to fuse logically conflicting content and yield unreliable representations. To address this, we propose LLM-TKT, a novel framework that distills LLM-based narrative reasoning into lightweight GNNs for robust fake news detection. The framework operates in two stages. First, we construct an offline LLM-driven narrative hub to synthesize global propagation narratives and diagnose local node-level coherence. Second, we design a dual-level narrative alignment to learn the semantic invariance of propagation with the guidance of propagation narratives. It filters unreliable neighbor nodes via local consistency and optimizes graph representations via global anchoring. Experiments on three real-world datasets demonstrate that LLM-TKT significantly outperforms existing methods, particularly in defending against sophisticated LLM-driven injection attacks without incurring runtime LLM inference costs.