Cognitive distortions are explicitly defined as a thinking pattern that occurs regardless of reality...that is why it is a distortion. Referring to a specific example makes no sense because it is a pattern of thought. Referring to reality makes no sense because the thought occurs regardless of reality.

As an example, a hypochondriac will believe they are sick when they are not. That does not mean one should not feel anxious about being sick, it means that one should not feel anxious about being sick when you have no evidence that you are sick. The reason for observing that such a person has cognitive distortions is to examine the impact of those thoughts on feelings and behaviour, not engage in a debate about the meaning of reality. Most of these distortions occur in people who are have poor mental health, it is not academic, it is a clinical treatment.

If you are curious, read more about CBT rather than jumping to conclusions wildly. You can disagree with the theory of mind used, but what you have said seems to misunderstand fundamentally what the paper is about.

Mental illness is not passion. Cognitive distortion do not mean someone is mentally ill, people can have all kinds of thoughts that are not based in reality with no impact on their life. At the same time, cognitive distortions can be ruinous for other people. Would you say someone with anorexia was just very passionate about winning their joust with Reason? No. Again, the point of "cognitive distortions" is the idea that your thoughts impact your feelings and behaviour which can lead to poor mental health if those thoughts are not accurate in some way. There are several very common cognitive distortions that occur with anxiety and depression, for example, which should indicate that they are not totally fictional.

Also, I am not really sure why this is controversial or unexpected. Some of the most common cognitive distortions are word-for-word how people explain what the OP calls "safetyism"...it shouldn't be a massive surprise. It is quite reasonable to ask whether everyone else in society needs to adjust their behaviour (to be clear, everyone can adjust their behaviour ad infinitum, it will make no difference to how these people feel...I think it is self-evident that increasing "awareness" or whatever has actually added to the anxiety because the media has taken the view that good journalism is triggering...it is unbelievably toxic, whether this stuff makes you unusually upset or not, ironically I know a psychologist who is remarkably even-handed and they stopped reading the news because they felt it made their life worse...again, is this helping anyone? It is just a race to the bottom).