Large language models (LLMs) have demonstrated impressive capabilities in utilizing external tools. In practice, however, LLMs are often exposed to tools that are irrelevant to the user's query, in which case the desired behavior is to refrain from invocations. In this work, we identify a widespread yet overlooked mechanistic flaw in tool refusal, which we term structural alignment bias: Even when a tool fails to serve the user's goal, LLMs still tend to invoke it whenever query attributes can be validly assigned to tool parameters. To systematically study this bias, we introduce SABEval, a new dataset that decouples structural alignment from semantic relevance. Our analysis shows that structural alignment bias induces severe tool-invocation errors in LLMs, yet remains largely unaccounted for in existing evaluations. To investigate the internal mechanisms underlying this bias, we propose Contrastive Attention Attribution, which reveals two competing pathways for semantic checking and structural matching. The relative strength of these pathways drives LLMs' tool invocation decisions. Based on these findings, we further introduce a rebalancing strategy that effectively mitigates structural alignment bias, as demonstrated by extensive experiments, without degrading general tool-use capabilities.