It's an insolvable problem, I think, and censorship is certainly not the right way to approach it. I may be wrong, but I believe a combination of 1) severe distrust of any form of media, 2) a healthy dose of criticism, 3) a wide range of sources of information, can somewhat help to reduce the issue. 1) and 2) require proper education, and 3) is about having a healthy journalistic landscape (i.e. lots of viewpoints and many ways to exchange them).
How do you suppose one should function, if one approaches every single sentence of every published news (which I think includes research as well) as being possibly untrue (which, I assume, is what's meant by severe distrust)? If there are no credible sources, how can you know anything about this world with any degree of certainty, then?
I have taken to reading a large number of individual sources, identifying the more trustworthy ones over time, and trusting primarily those sources. When one of them shifts to publishing propaganda (it is often a sudden unexplainable shift) then I write them off and remove them from my feed. Often I'll discover new sources through the networks of trusted sources.
This is very inefficient and I wish there were a better way to do it. It's not a perfect system, but it works well enough for me.
You used to be able to trust media institutions, as long as you knew their biases, but even basic facts are in question now and a great deal of so-called news is completely factless. (Headline: "Why politician X might be doing something illegal, maybe" with of course no facts to back up the supposition)
Media is flailing around searching for a sustainable business model, but it isn't working yet. Until they find something, I think we're stuck with bought-and-paid-for propaganda.
To me the answer lies in having access to a large variety of sources. The probability of false information goes down as decentralization of information goes up. For example, if you watch 10 people doing a live streaming event of a demonstration, you are probably going to have a better understanding of the event than from a single reporter on a major TV channel.
Of course, this means you can't fact-check everything because it would be way too much time consuming. So personally I live largely by ignoring the mass media and admit that I dont really know what is going on in most places besides very basic piece of news, and I certainly dont have enough information to have an opinion either.
"One man's terrorist is another man's freedom fighter" translates to "one person's information is another person's propaganda."