I don't know if it's really a matter of "trusting" the government, but of accepting that they already have access to most of my data anyway. Between credit cards, IP logs, subpoenas, national security letters, warrantless wiretapping, etc., they already know everything there is to know about me.
What makes this tradeoff (of convenience vs privacy) acceptable to me is not that I trust the government, but that I already accept I have near-zero privacy right now, as it is. Making it slightly easier for them isn't a big deal. I'm not a very exciting person to begin with.
And frankly I suspect that outside of techno-libertarian echo chambers, this is the case for most regular people. They just don't really care if the government knows about them. Not everyone has the same degree of desire/need for privacy.
