> That's a decision people can make without knowing the specifics of what kind of surveillance the government is doing.
I don't think it is. To make that decision you have to know the cost of secret abuses. And how are you supposed to know that if they're secret?
To make the reductio ad absurdum, suppose the government's line is that a plague that becomes contagious before it becomes symptomatic is ravaging the population and everyone is being tested and the people infected are immediately taken to quarantine where they uniformly die of the plague, but in reality what's happening is that genocidal fanatics in the government are doing genetic testing and sending people to death camps.
There is no amount of undermining security that can overcome that amount of harm. But if people are assuming that the harm is dramatically less than that and are not allowed to be corrected then they can't be expected to make the right decision.