Don't mistake governments with the state, or public institutions.
For instance, here in Germany, we have what U.S. people would probably call 'socialized health care'. We invented it, basically.
But this doesn't mean it's one gigantic insurance for all people. Actually, it's a system with hundreds of insurances, and you can pick the one you'd like (with some exceptions). The only thing you can not do is to not pick any of them. And no insurances is able to reject you.
The insurances may be companies, but there are also non-profit entities. Either way, they are separate from government. Strictly speaking, they aren't even part of the state. As far as I know no one from the government is allowed to request their files without a court order.
Additionally, there's a parallel 'free' system for people with sufficient income, and some special groups. Interestingly, civil servants seem to be one of these special groups. They may opt-in into the social system, but most of them seem to use the 'free' system -- not because of fear but because it's cheaper for them.
It's not a huge deal over here but imagine trying to run for office with an abortion from your 20's in your medical history if the opposition knew about it
Or politicians 'requesting' donations from directors of big companies or else their socially embarrassing medical issues like HIV (one in 20 people in the USA!) or plastic surgery history get's 'anonymously leaked'
Medical records can actually be a pretty huge source of power and that's certainly one thing the government should have as little as absolutely required of. All I have is a couple of broken bones in mine but I'm sure there are good people who could be swayed by bad people with the wrong information in the wrong hands
I don't want anyone snooping around my medical history, except myself. My doctor should only have the right to look at my paper history or my iPad (with secure, offline data).
Don't assume governments are more or less evil than companies. Losing control of your own data is the problem here.
