In Sweden, most patients are recruited into biobank research by non‐researcher doctors. Patients' trust in doctors may therefore be important to their willingness to participate. We suggest a model of trust that makes sense of such transitions of trust between domains and distinguishes adequate trust from mistaken trust. The unique position of doctors implies, we argue, a Kantian imperfect duty to compensate for patients' mistaken trust. There are at least three kinds of mistaken trust, each of which requires a different set of countermeasures. First, trust is mistaken when necessary competence is lacking; the competence must be developed or the illusion dispelled. Second, trust is irrational whenever the patient is mistaken about his actual reasons for trusting. Care must therefore be taken to support the patient's reasoning and moral agency. Third, some patients inappropriately trust doctors to recommend only research that will benefit them directly. Such trust should be counteracted by nurturing a culture where patients expect to be asked occasionally to contribute to the common good.