You might be able to overcome this by using a many-to-many authentication mechanism. But realistically, what could the government hope to accomplish by feeding you false information? (this is the only thing they are likely able to do). Consider:
There is no way to back track traffic and discover who sent the request.
Once you realize a source is feeding false information, you know to never trust that source again.
It is easy to imagine a decentralized rating system for the quality of information provided by various keys on the network. Keep in mind you can't really fake who you are. You are your public key, no one else can publish under your public key but you.
EDIT: I highly recommend reading the freent paper: http://freenetproject.org/papers/ddisrs.pdf
If you control a vast majority of the nodes, this is simply incorrect.
This is how freenet works. Of course, in freenet there is a time to live associated with each request so it will die eventually if, for example, the searched for item is not present on the network at that time. You could figure out that it's from a particular node by seeing what the time to live is from that node, but small amounts of random variance in time to live values can effectively ensure that both requests don't live forever and that it is suitably difficult to determine the origin of the requesting node.
Now, it is certainly possible with enough concerted effort to find out what a user is doing with some statistical probability that a user is looking at something, but you can rarely be absolutely sure.
And in other situations where people might want to use a darknet (e.g. a repressive regime) a few false positives aren't going to bother anyone concerned.
Unless you live in a predominantly authoritarian state (and I guess disagreement about this is what most of these discussions come down to, in the end), keeping government in check by empowering the people with insight and access to its processes is usually what enables a democracy.
Your point about darknet traffic being inherently more interesting is insightful, but I'm not sure where it gets us. The same can be said about TOR (and there have been attacks on this, too, as well as TOR posing the same issue of possibly being 'infected' by too many nodes of a single attacker) and I guess it' really just a technical challenge, in the end.
I would much prefer a network that piggybacks on the existing infrastructure and poses as innocuous traffic through stenography or encryption.