Clinical decision-making often begins with underspecified information and requires not only gathering missing information but also knowing when to stop. This calls for judging determinability (whether the available information is sufficient for a decision) by considering whether missing information could change the conclusion, not simply the amount of available decision-relevant information. Reliance on this amount as a cue for determinability, which we term \textit{factor coverage bias}, could undermine the trustworthiness of large language models (LLMs) through premature conclusions or excessive information gathering, such as unnecessary invasive tests. Yet whether LLMs exhibit this bias remains insufficiently studied. To address this gap, we construct a controlled pairwise benchmark in which LLMs identify the determinable case within each determinable--undeterminable pair. We add a decision-relevant factor to either side while keeping each case's determinability unchanged, and similarly add irrelevant text to distinguish this bias from context-length effects. Adding a relevant factor made LLMs more likely to select the augmented case as determinable even when it remained undeterminable, an effect that persisted with increased reasoning effort, while adding irrelevant text made them less likely to select the augmented case, an effect that reasoning substantially reduced. These findings identify factor coverage bias as a failure mode distinct from context-length effects and a potential risk to LLM trustworthiness. Our work provides an evaluation framework for LLM trustworthiness under underspecification.

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