This seems a bit paranoid to me. The government can listen in on people's internet activity without help from google, if they choose, but there is such a flood of information on the net it's of doubtful use unless they have some other reason to want to nail someone.
"The government can listen in on people's internet activity without help from google, if they choose"
Really? How can they do that?
Sure, they can go to the ISP of the person and track their online activity but that isn't what you are referring to, is it?