That's not the point of the study. Many negative thoughts are safe to ignore. There's a difference in dealing with realitiy and wallowing in negativity for its own sake, or because of some freudian bullshit.
Be that as it may, there is a big difference between not wallowing and ignoring/suppressing something. Especially if you leave Freud out.
https://www.merriam-webster.com/dictionary/suppress
Suppression implies force and a struggle. Its quite different from not dwelling.
I am pretty sure we are talking two ends of the same spectrum with an upper and a lower bound. The reason its worth pointing out is that the simplification otherwise creates new problems due to overcorrecting. While not pointlessly dwelling on negative stuff is certainly good advice, it doesnt mean suppressing negative stuff you havent dealt with is a good idea in the long run. Suppressing the knowledge of information that create negative emotions is a bad idea since its very likely valuable information you will need in the future to not repeat your mistakes. One is a problem with agency over emotions and reactions, one is a practical functional problem.
I think the reference to Freud and suppression might be a not thought through attention grab on part of the authors. Different to what their press statement says, what they have found does not run counter to accepted narratives. While i sympathize with the need for funding, this is a dumb spin.
For example, depression is often characterized by black and white thinking and getting tunnel vision. You become so focused on the worst things you can come up with being true that you loose sight of your perspective being incomplete and the stress makes it harder and harder to snap out. Which results in either incomplete or erroneous conclusions you still hold with conviction. After all, you know X to be true and as a result that you are doomed to experience Y. So unless you are the only human not functioning this way, you have good chances of changing your experience without resorting to supression.
I think the difference in dealing with these patterns manifesting comes from insight. You can try to suppress that initial bad insight temporarily or you can come to terms what is happening to you and how much you should care about what at which time. A lot easier said then done sure, but going full suppression seems like really bad advice. Be it through distraction or a bottle, you sooner or later will be confronted with a distorted self image again.
At that point you are getting countermeasures for distortions and unrealistic expectations. You might get used to them, but they were just distortions. Getting used to them might have not been a good idea. Even if you reduce suffering, you are establishing a new higher normal.
I get that this sounds a lot like Freud, but i am looking at this more from a human error perspective. Its not much different from cognitive biases, its part of how the mind comes to erroneous / incomplete conclusions and how these can create negative feedback loops. Making the first step suppression instead of introspection seems really counterproductive. You are kind of stuck with your brain and might as well optimize some. Some agency is achievable and it often doesnt need to be hard. No sense in being sad about your brain being buggy. Brains just are.