How to build trust I think is your basic question.
It depends on the situation you have in your country. In Estonia, coming from this totalitarian system where Big Brother was watching us all the time, and our own government, it was such a different situation that we didn't even ask if we should be concerned that our own government would misuse our data. This problem of non-trust has been so strong in Estonia, as I understand it, but still people should know how a system works. With their having this concern, government should be able to explain what is behind this data exchange and how citizens' data is protected. There is lots of work there, and there is a rising need for that.
However, once again, paper documents are much more unsecure than digital information.