Confidence in the health care system implies an expectation that sufficient and appropriate treatments will be provided if needed. The COVID-19 public health crisis is a significant, global, and (mostly) simultaneous test of the behavioral implications arising from this confidence. We explore whether populations reporting low levels of confidence in the health care system exhibit a stronger behavioral reaction to the COVID-19 pandemic. We track the dynamic responses to the COVID-19 pandemic across 38 European countries and 621 regions by employing a large dataset on human mobility generated between February 15 and June 5, 2020 and a broad range of contextual factors (e.g., deaths or policy implementations). Using a time-dynamic framework we find that societies with low levels of health care confidence initially exhibit a faster response with respect to staying home. However, this reaction plateaus sooner, and after the plateau it declines with greater magnitude than does the response from societies with high health care confidence. On the other hand, regions with higher confidence in the health care system are more likely to reduce mobility once the government mandates that its citizens are not to leave home except for essential trips, compared to those with lower health care system confidence. Regions with high trust in the government but low confidence in the health care system dramatically reduce their mobility, suggesting a correlation for trust in the state with respect to behavioral responses during a crisis.