I mean, we're already in a world where a large percentage do not trust anything the media is saying. Where 'CNN is fake news' is basically a meme and 'alternative' news publications have taken a large bite out of the older ones' markets.
If they try and paint the trucker actions as all negative or crazy, it could go about as well as painting Trump crazy did prior to the 2016 election. Or pleading for Britain to stay in the EU pre Brexit.
And something similar also led to GamerGate becoming such a catastrophe.
If the media try anything like this against the general population, they'll soon notice that:
1. Trust in them will decline even further 2. Alternative news sites and YouTube influencers will take full advantage of the situation and cover the other side extensively. 3. They'll turn social media sites into even more of a war zone than they already are.
So unless they want Breitbart (or the next Breitbart equivalent) to gain a few thousand times more traffic from people who feel like 'the media' is lying to them, I doubt they'll continue this sort of path.