Would you really trust government-controlled internet provider? I'm not usually one to spout conspiracy theories, but even I'd be unable to prevent doubts about the content coming through it.
I don't really think there's a difference between what we have right now and a government-controlled provider. The major backbones are already working hand-in-hand with the government, major news sources are working with the government, social news sites have government-published stories. There's no way to validate that anything isn't from the government on the Internet.
The only difference would be in perception, not in reality.
I don't know that I agree with your first paragraph, but validation of what's from the government isn't the only problem. In the internet age, freedom of speech effectively requires internet access. If the government can boot you off the internet or ban your content, that's a major blow to freedom of speech.
The only difference would be in perception, not in reality.