It is not hard to distrust media and have reasons not to trust it. For one, when everyone has different views, news becomes bias. But also, when someone speaks out against something, you can start seeing what is fake and what is over exaggerated.
As far as the second part you said, I think the boundary is when these things start to be politisized and government controlled.
Distrust is a consequence of the Fall. Jesus gave us the antidote, which is faith. Approaching life with a measure of faith allows us to learn new ideas and develop trust in the wheat after we discard the chaff.
Faith is the space between our reason and a new concept, whether it be God or something mundane. Kierkegaard (Christian and father of existentialism), talks about the need to take a leap of faith once we get to the end of reasoning. After we take this leap, we will discover if the concept is truth or a falsehood. I have found faith in Jesus Christ to be fruitful and Him to be trustworthy.
Faith, like every other concept Jesus taught to His disciples was already part of the human condition - it was in our wheelhouse, so to speak. If it was not, we would not be able to understand or make use of it. Yes, it is a gift from God, but it is more like He is redirecting our faith from self to Him, rather than giving us a brand new tool.
So, the process for determining truth appears to be; Reason + Leap of Faith + Revelation = outcome - determining truth from falsehood