The rapid growth of short video platforms has made multimodal fake news more prevalent. Existing detectors suffer from two major limitations: (I) global-alignment bias that overemphasizes holistic cross-modal matching and thus misses subtle, localized inconsistencies; and (II) LLM-based methods that leverage powerful generative reasoning to identify cognitive forgeries but inherently suffer from hallucinations and high inference latency. To overcome these limitations, we propose PCDD, a novel Perception-Cognition Dual-driven Detector that jointly observes the form and probes the logic for short video fake news detection. The perception stream exposes fine-grained cross-modal conflicts by amplifying localized inconsistencies into explicit discrepancies. The cognition stream transfers reasoning capabilities from LLMs to a lightweight student to mine cognitive forgeries, while reducing the risk of hallucinations and eliminating reliance on LLMs at inference. Experiments on real-world datasets show that PCDD consistently outperforms baselines, while improving interpretability and robustness in data scarcity scenarios. Our code is available at: https://github.com/SeinCore/PCDD.