None of your hypos are similar to what I proposed. Mainly because in those situations "not playing into the government's hand" has no negative consequences.
In my hypo you would want to not "play into the government's hand" simply out of self-interest. To avoid dying.
My point, if I had one, is that while one can imagine a conspiracy theory whose direct implication is "I should not get vaccinated", one can just as easily imagine a conspiracy theory whose direct implication is "I <i>should</i> get vaccinated."
If the latter theory is no less credible than the former, given the bizarre assumptions most conspiracy theorists make, then on what basis does he assume the former and avoid vaccination?