Suppressing negative thoughts is a fool’s errand. You can notice them, and react differently to them, but you can’t literally control the thoughts that arise in your consciousness. You’ll work yourself to death trying.
I do not like the article's use of "suppress" as it is an active and forceful word, that connotes some sort of combat or struggle over the thoughts. It's the struggle that will get you in trouble.
It also depends on the nature of the thoughts and our relationship to them. Sometimes we need to work through negative events, process them, deal with them. This study appeared to focus on future imagined events, which are clearly different, and many of us fall victim to catastrophizing, ruminating, and worrying about things that may never happen, or things over which we have no control.
Practicing centering prayer, or mindfulness meditation, it is a discipline to master our thoughts and not allow them to dominate us. Rather than "suppressing" negative thoughts, they can just be neutrally acknowledged, and released without engaging them. In fact, all manner of thoughts and ideas can be treated this way during a meditation, and we will find that nothing in our mundane lives is so important or devastating that it could take the place of God.
But yes, you can get to a certain age, and with a lack of developed discipline, you will feel trapped and powerless to "control" those thoughts, and the first attempts will feel futile. But it's certainly possible and achievable.