I think this would be the natural solution to the problem we see in cult behavior, to prevent the cult from spreading it's mental illness via playing on paranoia by limiting news to facts rather than an attempt to provoke an emotional reaction but as you predict, I think the purveyors will just find another way. What this tells me is that the problem is not in the lies themselves, they can be anything, but in what I would call a fact, that there is within people a need to believe. In short, in my opinion, people don't so much have a gullibility problem they fall pray to, but that they actually want to be lied to, that what they really crave is the feeling of being OK. That is where both the truth and the lie is. They are OK but they neither know it nor feel it inwardly and crave outside validation, some imaginary authority do god to tell them they are. What we crave is to feel special, entitled, and we don't much care how we get it. Even being deplorable is just fine if someone else is telling us that being deplorable is a good thing, if all of 'us true believers' are the real people.
Nobody wants to know how emotionally needy they are, how dependent they are on others for self confidence, how badly we seek validation, and especially how hollow we are inside, how vacuous and empty our lives really are lacking the one and only thing of real value there is, real self respect. Nobody even has any idea what that is.
So, in my opinion, what America needs is psychological education but because nobody wants to see the hole within themselves and feel the pain of separation and internal division or give up their attachment to the phony ego they feel so good about, thin basic kind of self awareness will remain hidden, known only to those who can't live without it. There are always those who will be fixated on the mystery of the Matrix for use of a modern metaphor.