Honestly I think that there is quite a lot of non-fearmongering media out there. The Economist strikes me as a good example. And in general I think if you read any "respectable" (Economist, NYT, WSJ, WaPo, La Monde, etc.) newspaper as a whole on a day-to-day basis you wouldn't come away from the experience being especially scared or fearful. The problem is that it all gets dumped into the social media slurry and what a lot of people consume (in practice) is a sort of curated selection of the most sensationalist individual stories across the entire media ecosystem.
I think one dimension of crisis mongering is how drastic the stakes are portrayed. Its one thing to discuss discerning trends or potential problems, and another to portray every problem as a struggle of between good and evil in which the balance of the universe hangs. The Economist tends to stick to the former side of the spectrum than the latter in my experience.