Hallucinations in video-capable vision-language models (Video-VLMs) remain frequent and high-confidence, while existing uncertainty metrics often fail to align with correctness. We introduce VideoHEDGE, a modular framework for hallucination detection in video question answering that extends entropy-based reliability estimation from images to temporally structured inputs. Given a video-question pair, VideoHEDGE draws a baseline answer and multiple high-temperature generations from both clean clips and photometrically and spatiotemporally perturbed variants, then clusters the resulting textual outputs into semantic hypotheses using either Natural Language Inference (NLI)-based or embedding-based methods. Cluster-level probability masses yield three reliability scores: Semantic Entropy (SE), RadFlag, and Vision-Amplified Semantic Entropy (VASE). We evaluate VideoHEDGE on the SoccerChat benchmark using an LLM-as-a-judge to obtain binary hallucination labels. Across three 7B Video-VLMs (Qwen2-VL, Qwen2.5-VL, and a SoccerChat-finetuned model), VASE consistently achieves the highest ROC-AUC, especially at larger distortion budgets, while SE and RadFlag often operate near chance. We further show that embedding-based clustering matches NLI-based clustering in detection performance at substantially lower computational cost, and that domain fine-tuning reduces hallucination frequency but yields only modest improvements in calibration. The hedge-bench PyPI library enables reproducible and extensible benchmarking, with full code and experimental resources available at https://github.com/Simula/HEDGE#videohedge .