Large language models perform well on medical examinations, but users routinely challenge their answers and invoke professional roles, and it is unclear what a system does when a medical credential and a stated task-specific accuracy point in opposite directions. In a factorial experiment on 480 items from four Polish specialty examination sets and three consumer large language model systems (ChatGPT, Claude, Gemini), each item and system received eleven independent conversations. Conditions crossed attributed source role (medical student, experienced specialist), stated prior accuracy on similar questions (2/10, 8/10) and suggestion correctness. The primary outcome was adoption of a prespecified incorrect option when the baseline answer matched the official key, comparing a specialist described as 2/10 with a student described as 8/10. Baseline agreement with the key was 87.2% across 15,683 analyzable conversations. The incorrect option was adopted more often from the specialist described as 2/10 than from the student described as 8/10 (10.2% vs. 7.6%; adjusted risk difference +2.82 percentage points, 95% CI +0.65 to +4.99). Estimates varied across the three systems and only one system-specific interval excluded zero. In a prespecified exploratory analysis with a shared eligibility rule, correct suggestions were adopted far more often than incorrect ones (risk difference +35.7 percentage points, 95% CI +30.8 to +40.7), indicating selective rather than indiscriminate compliance. An incorrect suggestion from a specialist with low stated accuracy was therefore slightly more influential than the same suggestion from a student with high stated accuracy, although the difference was modest and varied across systems. Agreement reached only after a user has disclosed a preferred answer should not automatically be treated as an independent second opinion, and medical large language model systems should be evaluated on how they revise answers after such disclosure, not solely on initial accuracy.