Some vaccine-hesitant people lack epistemic trust in the COVID-19 vaccine recommendation that because vaccines have been shown to be medically safe and effective, one ought to get vaccinated. Citing what I call exception information, they claim that whatever the general safety and efficacy of vaccines, the vaccines may not be safe and effective for them. Examples include parents citing information about their children's health, pregnant women's concerns about the potential adverse effects of treatment on pregnant women, young people citing their relative invulnerability to extreme COVID-19 symptoms, or members of vulnerable racial groups citing epistemic injustice, such as a lack of representation in COVID-19 vaccine trials. This paper examines the extent to which a lack of epistemic trust in vaccine recommendations, based on such exemption information, is rational.