Question: Does atomic fact-checking, which decomposes AI treatment recommendations into individually verifiable claims linked to source guideline documents, increase clinician trust compared to traditional explainability approaches? Findings: In this randomized trial of 356 clinicians generating 7,476 trust ratings, atomic fact-checking produced a large effect on trust (Cohen's d = 0.94), increasing the proportion of clinicians expressing trust from 26.9% to 66.5%. Traditional transparency mechanisms showed a dose-response gradient of improvement over baseline (d = 0.25 to 0.50). Meaning: Decomposing AI recommendations into individually verifiable claims linked to source guidelines produces substantially higher clinician trust than traditional explainability approaches in high-stakes clinical decisions.