An interesting comment. The assumption here is that the more people get the benefit less people will distrust. This logic works if people realised why vaccine works and in that case there would be a positive correlation not negative as more people understand more people get vaccinated. The distrust happens because people get “protected”, or they do not get to “see the effect” because preemptive protection is not visible. What happens though is when people experience vaccine side effects, they become vaccine skeptics. So the more people get vaccinated (by government action or social coercion), the more likely that side effects would result at least for some, the more in the number of distrustful people or vaccine skeptics.