With how governments have behaved I absolutely understand why people would distrust them and to be honest, I have absolutely zero trust in government right now too. They put politics and driving wedges between people to further entrench their positions (a bunch of provinces and our feds all called snap elections during Covid) over honesty and people. Even now instead of trying to assuage the fears of the vaccine hesitant, they just demonise and threaten them.
Personally, the only trust I have is that a bunch of PhDs making vaccines care about solving a hard problem, so I got the vaccine. Not that I was ever worried about Covid itself, I had Covid during wave 1, had contact with a bunch of Covid positive people in wave 2 without contracting it again, etc...