> People should be encouraged to trust their intuition

The proliferation of fake news doesn't do that. Fake news just reinforces people's biases as they self-select to read a fake news outlet that they agree with, killing any remainder of sceptisism and critical thinking.

> People should be encouraged to trust their intuition even if it occasionally leads them to make mistakes.

That's how it works with real, good-but-not-perfectly-impartial news. Fake news on the other hand is almost entirely lies that remain unquestioned by its consumers, resulting in many many more "mistakes".