Enhancing the reasoning capabilities of Large Language Models (LLMs) is a key strategy for building Agents that "think then act." However, recent observations, like OpenAI's o3, suggest a paradox: stronger reasoning often coincides with increased hallucination, yet no prior work has systematically examined whether reasoning enhancement itself causes tool hallucination. To address this gap, we pose the central question: Does strengthening reasoning increase tool hallucination? To answer this, we introduce SimpleToolHalluBench, a diagnostic benchmark measuring tool hallucination in two failure modes: (i) no tool available, and (ii) only distractor tools available. Through controlled experiments, we establish three key findings. First, we demonstrate a causal relationship: progressively enhancing reasoning through RL increases tool hallucination proportionally with task performance gains. Second, this effect transcends overfitting - training on non-tool tasks (e.g., mathematics) still amplifies subsequent tool hallucination. Third, the effect is method-agnostic, appearing when reasoning is instilled via supervised fine-tuning and when it is merely elicited at inference by switching from direct answers to step-by-step thinking. We also evaluate mitigation strategies including Prompt Engineering and Direct Preference Optimization (DPO), revealing a fundamental reliability-capability trade-off: reducing hallucination consistently degrades utility. Mechanistically, Reasoning RL disproportionately collapses tool-reliability-related representations, and hallucinations surface as amplified divergences concentrated in late-layer residual streams. These findings reveal that current reasoning enhancement methods inherently amplify tool hallucination, highlighting the need for new training objectives that jointly optimize for capability and reliability.