That's also exactly why these sectors suffer from way above average depression rates, even tho most of them have the training, knowledge and, ideally, access facilities that should help them deal with it better.
But it's not simple as you make it out to be: Humans are emotional beings, whether we like that or not, it's not something we can "train away" or just turn off on demand, it's part of what makes us humans.
What training helps with is staying clear and sober in the moment where it counts, but that does not negate the long-term impact of regularly being exposed to such situations and the emotional toll they excerpt; It adds up, and creeps back up in the most irrelevant contexts.
To bring it back to the topic: When participants rationally knew the source and thus most likely the claim to not to be credible, even with that rational knowledge, the headline still ended up having an emotional impact on them.
Which will very likely add up over time just as it does with social jobs, but trying to evade that impact seems impossible: There is no way to know if a headline is emotional until actually reading and parsing it, but by that point it's apparently already too late.
But it's not out of reach for a person who just practices it consciously. This is not about removing your emotions, it's about letting your mind observe the flow of emotions, and still stay and act sober.