The statement "The earth is flat" is factually inaccurate, but if someone truly believes and argues in its favor, it is not deceptive. Research on deception detection and fact checking often conflates factual accuracy with the truthfulness of statements. This assumption makes it difficult to (a) study subtle distinctions and interactions between the two and (b) gauge their effects on downstream tasks. The belief-based deception framework disentangles these properties by defining texts as deceptive when there is a mismatch between what people say and what they truly believe. In this study, we assess if presumed patterns of deception generalize to German language texts. We test the effectiveness of computational models in detecting deception using an established corpus of belief-based argumentation. Finally, we gauge the impact of deception on the downstream task of fact checking and explore if this property confounds verification models. Surprisingly, our analysis finds no correlation with established cues of deception. Previous work claimed that computational models can outperform humans in deception detection accuracy, however, our experiments show that both traditional and state-of-the-art models struggle with the task, performing no better than random guessing. For fact checking, we find that Natural Language Inference-based verification performs worse on non-factual and deceptive content, while prompting Large Language Models for the same task is less sensitive to these properties.